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NCERT Class X Chapter 5: Arithmetic Progression Example 2(iv) Question: Which of the following list of numbers form an AP? If they form an AP, write the next two terms 1, 1, 1, 2, 2, 2, 3, 3, 3, . . . Given: The sequence: 1, 1, 1, 2, 2, 2, 3, 3, 3, . . . To Find: Whether the given sequence forms an arithmetic progression (AP). If it does, find the next two terms. Formula: In an AP, the difference between consecutive terms is constant (common difference). Solution: Let the given list of numbers be a1, a2, a3, a4, ... Then, a1 = 1  a2 = 1  a3 = 1 a4 = 2 a5 = 2 a6 = 2 a7 = 3 a8 = 3 a9 = 3  Lets calculate the common difference, d = a2 - a1 = 1 - 1 = 0 d = a3 - a2 = 1 - 1 = 0 d = a4 - a3 = 2 - 1 = 1 The common difference changes and hence it is not a constant.  Hence, the sequence is not an AP because the difference between consecutive terms is not constant.  Result: The given sequence 1, 1, 1, 2, 2, 2, 3, 3, 3, . . . is not ...

NCERT Class X Chapter 5: Arithmetic Progression Example 2(iii) Question: Which of the following list of numbers form an AP? If they form an AP, write the next two terms -2,2,-2,2,-2, . . . Given: The sequence is -2, 2, -2, 2, -2, . . . To Find: Whether the given sequence forms an AP. If it does, find the next two terms. Formula: In an Arithmetic Progression (AP), the difference between consecutive terms is constant.  This constant difference is called the common difference (d). Solution: Let's examine the differences between consecutive terms: 2 - (-2) = 4 -2 - 2 = -4 Since the differences are not constant (4 and -4), the sequence does not have a common difference. Therefore, the given sequence is not an arithmetic progression. Result: The sequence -2, 2, -2, 2, -2, ... is not an arithmetic progression. Next question solution: NCERT Class X Chapter 5: Arithmetic Progression Example 2 (iv). Explore more in Arithmetic Progressions...

NCERT Class X Chapter 5: Arithmetic Progression Example 2(ii) Question: Which of the following list of numbers form an AP? If they form an AP, write the next two terms : 1, – 1, – 3, – 5, . . . Given: The list of numbers is 1, –1, –3, –5, . . . To Find: Whether the given list of numbers forms an arithmetic progression (AP). If it forms an AP, find the next two terms. Formula: In an arithmetic progression, the difference between consecutive terms is constant.  This constant difference is called the common difference (d). Solution: Let the given list of numbers be denoted by a 1 , a 2 , a 3 , a 4 , ... Then, a 1 = 1, a 2 = –1, a 3 = –3, a 4 = –5, ... Let's find the common difference (d): d = a 2 – a 1 = –1 – 1 = –2 d = a 3 – a 2 = –3 – (–1) = –2 d = a 4 – a 3 = –5 – (–3) = –2 Since the common difference is constant (d = –2), the given list of numbers forms an arithmetic progression. ...

NCERT Class X Chapter 5: Arithmetic Progression Example 2(i) Question: Which of the following list of numbers form an AP? If they form an AP, write the next two terms : (i) 4, 10, 16, 22, . . . Given: The list of numbers is 4, 10, 16, 22, . . . To Find: 1. Whether the given list of numbers forms an AP.  2. If they form an AP, find the next two terms. Formula: In an Arithmetic Progression (AP), the difference between consecutive terms is constant.  This constant difference is called the common difference (d). Solution: Let the given list of numbers be a 1 , a 2 , a 3 , a 4 , ... a 1 = 4 a 2 = 10 a 3 = 16 a 4 = 22 Let's find the common difference (d): d = a 2 - a 1 = 10 - 4 = 6 d = a 3 - a 2 = 16 - 10 = 6 d = a 4 - a 3 = 22 - 16 = 6 Since the common difference is constant (d = 6), the given list of numbers forms an AP. To find the next two terms, we add the co...

NCERT Class X Chapter 5: Arithmetic Progression Example 1 Question: For the AP: 3/2, 1/2, -1/2, -3/2,.... write the first term a and common difference d Given: The Arithmetic Progression (AP) is: 3 2 , 1 2 , -1 2 , -3 2 , ... To Find: The first term (a) and the common difference (d) of the given AP. Formula: In an AP, the first term is denoted by 'a' and the common difference is denoted by 'd'. The common difference is calculated by subtracting any term from its succeeding term: d = a n+1 - a n Solution: The first term of the AP is a = 3 2 To find the common difference, we subtract the first term from the second term: d = a 2 - a 1   ⇒ d = 1 2 - 3 2   ⇒ d = 1 - 3 2   ⇒ d = -2 2   ⇒ d = -1 Result: First term (a) = 3 2 Common difference (d) = -1 Next question solution: NCERT Class X Chapter 5: Arithmetic Progression Exa...

NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.1 Question 4 (xv) Question: Which of the following are APs ? If they form an AP, find the common difference d and write three more terms. 1 2 , 5 2 , 7 2 , 73, . . , . . . Given: The sequence is 1 2 , 5 2 , 7 2 , 73, . . . This translates to 1, 25, 49, 73, ... To Find: Whether the given sequence is an AP. If it is, find the common difference (d) and the next three terms. Formula: In an arithmetic progression (AP), the difference between consecutive terms is constant. This difference is called the common difference (d). a n = a 1 + (n-1)d Solution: Let's find the difference between consecutive terms: 25 - 1 = 24 49 - 25 = 24 73 - 49 = 24 Since the difference between consecutive terms is constant (24), the sequence is an AP. The common difference, d = 24 To find the next three terms, we add the common difference (24) repeatedly: 73 + 24 = 97 97 + 24 = 121 121 + 24 = 145 Resu...

NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.1 Question 4 (xiv) Question: Which of the following are APs ? If they form an AP, find the common difference d and write three more terms. 1 2 , 3 2 , 5 2 , 7 2 , . . . Given: The sequence: 1 2 , 3 2 , 5 2 , 7 2 , . . . To Find: Whether the given sequence is an AP. If it is, find the common difference (d) and the next three terms. Formula: In an Arithmetic Progression (AP), the common difference (d) between consecutive terms is constant. d = a n+1 - a n Solution: The given sequence is: 1 2 , 3 2 , 5 2 , 7 2 , ... which is 1, 9, 25, 49, ... Let's find the differences between consecutive terms: 9 - 1 = 8 25 - 9 = 16 49 - 25 = 24 Since the differences are not constant, this is not an AP. Result: The given sequence is not an Arithmetic Progression (AP). Next question solution: NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.1 Question 4 (xv). Explore mo...

NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.1 Question 4 (xiii) Question: Which of the following are APs ? If they form an AP, find the common difference d and write three more terms. √3, √6, √9, √12, . . . Given: The sequence is √3, √6, √9, √12, . . . To Find: Whether the sequence is an AP. If it is, find the common difference (d) and the next three terms. Formula: In an Arithmetic Progression (AP), the difference between consecutive terms is constant. This constant difference is called the common difference (d). Solution: Let's check if the difference between consecutive terms is constant: √6 - √3 ≈ 1.464 √9 - √6 ≈ 0.816 √12 - √9 ≈ 0.667 Since the difference between consecutive terms is not constant, the given sequence is not an AP. Result: The sequence √3, √6, √9, √12, . . . is not an arithmetic progression. Next question solution: NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.1 Question 4 (xiv). ...

NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.1 Question 4 (xii) Question: Which of the following are APs ? If they form an AP, find the common difference d and write three more terms. √2, √8, √18, √32, ... Given: The sequence is √2, √8, √18, √32, ... To Find: Whether the given sequence is an AP. If it is an AP, find the common difference (d) and the next three terms. Formula: In an Arithmetic Progression (AP), the difference between consecutive terms is constant. This constant difference is called the common difference (d). Solution: Let the given sequence be denoted by a n . We have: a 1 = √2 = √(2 × 1 2 ) = √2 a 2 = √8 = √(2 × 2 2 ) = 2√2 a 3 = √18 = √(2 × 3 2 ) = 3√2 a 4 = √32 = √(2 × 4 2 ) = 4√2 The common difference is: d = a 2 - a 1 = 2√2 - √2 = √2 d = a 3 - a 2 = 3√2 - 2√2 = √2 d = a 4 - a 3 = 4√2 - 3√2 = √2 Since the common difference is constant (d = √2), the sequence is an AP. The next three terms are: a ...

NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.1 Question 4 (xi) Question: Which of the following are APs ? If they form an AP, find the common difference d and write three more terms. a, a 2 , a 3 , a 4 Given: Sequence: a, a 2 , a 3 , a 4 , ... To Find: Whether the given sequence is an AP. If it is an AP, find the common difference (d) and the next three terms. Formula: In an Arithmetic Progression (AP), the common difference (d) between consecutive terms is constant. d = a n+1 - a n , where a n is the nth term. Solution: Let's examine the differences between consecutive terms: a 2 - a = a(a - 1) a 3 - a 2 = a 2 (a - 1) Since a 2 (a - 1) ≠ a(a - 1) unless a = 1 or a = 0, the difference between consecutive terms is not constant. Therefore, the given sequence is not an Arithmetic Progression. Result: The sequence a, a 2 , a 3 , a 4 , ... is not an AP. Next question solution: NCERT Class X Chapter 5: Arithmetic Progressio...

NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.1 Question 4 (x) Question: Which of the following are APs ? If they form an AP, find the common difference d and write three more terms. a, 2a, 3a, 4a, . . . Given: The sequence: a, 2a, 3a, 4a, . . . To Find: Whether the given sequence is an AP. If it is, find the common difference (d) and the next three terms. Formula: In an AP, the common difference (d) is given by: d = a n - a n-1 , where a n is the nth term and a n-1 is the (n-1)th term. Solution: Let's find the difference between consecutive terms: 2a - a = a 3a - 2a = a 4a - 3a = a Since the difference between consecutive terms is constant and equal to 'a', the given sequence is an arithmetic progression (AP). The common difference is d = a. To find the next three terms, we add the common difference to the last term repeatedly: 5th term = 4a + a = 5a 6th term = 5a + a = 6a 7th term = 6a + a = 7a Result: Yes...

NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.1 Question 4 (ix) Question: Which of the following are APs ? If they form an AP, find the common difference d and write three more terms. 1, 3, 9, 27, . . . Given: The sequence: 1, 3, 9, 27, . . . To Find: Whether the given sequence is an AP. If it is, find the common difference (d) and the next three terms. Formula: In an Arithmetic Progression (AP), the difference between consecutive terms is constant. This constant difference is called the common difference (d). Solution: Let's check if the given sequence is an AP by finding the difference between consecutive terms: 3 - 1 = 2 9 - 3 = 6 27 - 9 = 18 Since the differences between consecutive terms are not constant (2, 6, 18), the given sequence is not an arithmetic progression (AP). Result: The given sequence 1, 3, 9, 27, . . . is not an AP. Next question solution: NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.1 ...

NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.1 Question 4 (viii) Question: Which of the following are APs ? If they form an AP, find the common difference d and write three more terms. -1/2, -1/2, -1/2, -1/2, ... Given: The sequence: -1/2, -1/2, -1/2, -1/2, ... To Find: Whether the given sequence is an AP. If it is, find the common difference (d) and the next three terms. Formula: In an Arithmetic Progression (AP), the common difference (d) is given by: d = a n+1 - a n , where a n+1 and a n are consecutive terms. Solution: Let's find the difference between consecutive terms: a 2 - a 1 = - 1 2 - (- 1 2 ) = 0 a 3 - a 2 = - 1 2 - (- 1 2 ) = 0 Since the difference between consecutive terms is constant (0), the sequence is an AP with a common difference d = 0. The next three terms are -1/2, -1/2, -1/2. Result: The sequence is an AP with common difference d = 0. The next three terms are -1/2...

NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.1 Question 4 (vii) Question: Which of the following are APs ? If they form an AP, find the common difference d and write three more terms. 0, – 4, – 8, –12, . . . Given: The sequence is 0, – 4, – 8, –12, . . . To Find: Whether the given sequence is an AP. If it is an AP, find the common difference (d) and the next three terms. Formula: In an arithmetic progression (AP), the difference between consecutive terms is constant. This constant difference is called the common difference (d). Solution: Let the given sequence be denoted by {a n }, where a 1 = 0, a 2 = -4, a 3 = -8, a 4 = -12, ... We calculate the differences between consecutive terms: a 2 - a 1 = -4 - 0 = -4 a 3 - a 2 = -8 - (-4) = -4 a 4 - a 3 = -12 - (-8) = -4 Since the difference between consecutive terms is constant and equal to -4, the given sequence is an arithmetic progression (AP). The common difference is d = -4...

NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.1 Question 4 (vi) Question: Which of the following are APs ? If they form an AP, find the common difference d and write three more terms. 0.2, 0.22, 0.222, 0.2222, . . . Given: The sequence is 0.2, 0.22, 0.222, 0.2222, . . . To Find: Whether the given sequence is an AP. If it is an AP, find the common difference (d) and the next three terms. Formula: In an AP, the common difference (d) between consecutive terms is constant. d = a n - a n-1 Solution: Let's find the differences between consecutive terms: 0.22 - 0.2 = 0.02 0.222 - 0.22 = 0.002 0.2222 - 0.222 = 0.0002 Since the differences between consecutive terms are not constant, the given sequence is not an arithmetic progression (AP). Result: The sequence 0.2, 0.22, 0.222, 0.2222,... is not an AP. Next question solution: NCERT Class X Chapter 5: Arithmetic Progression Exer...

NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.1 Question 4 (v) Question: Which of the following are APs ? If they form an AP, find the common difference d and write three more terms. 3, 3+√2, 3+2√2, 3+3√2,... Given: The sequence is 3, 3+√2, 3+2√2, 3+3√2,... To Find: Whether the given sequence is an AP. If it is an AP, find the common difference (d) and the next three terms. Formula: In an Arithmetic Progression (AP), the difference between consecutive terms is constant. This constant difference is called the common difference (d). Solution: Let the given sequence be denoted by {a n }. Then a 1 = 3, a 2 = 3+√2, a 3 = 3+2√2, a 4 = 3+3√2, ... We find the difference between consecutive terms: a 2 - a 1 = (3+√2) - 3 = 3 + √2 - 3 = √2 a 3 - a 2 = (3+2√2) - (3+√2) = 3 + 2√2 -3 -√2 = √2 a 4 - a 3 = (3+3√2) - (3+2√2) = 3 + 3√2 - 3 - 2√2 = √2 Since the difference between consecutive terms is constant and equal to √2, the given seque...

NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.1 Question 4 (iv) Question: Which of the following are APs ? If they form an AP, find the common difference d and write three more terms. – 10, – 6, – 2, 2, . . . Given: The sequence: –10, –6, –2, 2, . . . To Find: Whether the sequence is an AP. If it is, find the common difference (d) and the next three terms. Formula: In an Arithmetic Progression (AP), the common difference (d) is given by: d = a n - a n-1 , where a n is the nth term and a n-1 is the (n-1)th term. Solution: Let's find the differences between consecutive terms: –6 – (–10) = 4 –2 – (–6) = 4 2 – (–2) = 4 Since the difference between consecutive terms is constant (4), the sequence is an arithmetic progression (AP). The common difference, d = 4. To find the next three terms, we add the common difference successively: 2 + 4 = 6 6 + 4 = 10 10 + 4 = 14 Result: The sequence is an AP with a common difference d ...

NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.1 Question 4 (iii) Question: Which of the following are APs ? If they form an AP, find the common difference d and write three more terms. – 1.2, – 3.2, – 5.2, – 7.2, . . . Given: The sequence: – 1.2, – 3.2, – 5.2, – 7.2, . . . To Find: Whether the given sequence is an AP. If it is an AP, find the common difference (d) and the next three terms. Formula: In an AP, the common difference (d) is given by: d = a n - a n-1 , where a n and a n-1 are consecutive terms. Solution: Let's find the difference between consecutive terms: – 3.2 – (– 1.2) = –3.2 + 1.2 = –2 – 5.2 – (– 3.2) = –5.2 + 3.2 = –2 – 7.2 – (– 5.2) = –7.2 + 5.2 = –2 Since the difference between consecutive terms is constant and equal to –2, the given sequence is an arithmetic progression (AP). The common difference, d = –2 To find the next three terms, we add the common difference successively: – 7.2 + (–2) = –9.2 – 9.2 ...

NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.1 Question 4 (ii) Question: Which of the following are APs ? If they form an AP, find the common difference d and write three more terms. 2, 5/2, 3, 7/2, . . . Given: The sequence is 2, 5/2, 3, 7/2, . . . To Find: Whether the given sequence is an Arithmetic Progression (AP). If it is an AP, find the common difference (d) and the next three terms. Formula: In an AP, the common difference (d) between consecutive terms is constant. d = a n+1 - a n , where a n is the nth term. Solution: Let's find the differences between consecutive terms: 5/2 - 2 = 1 2 = 0.5 3 - 5/2 = 1 2 = 0.5 7/2 - 3 = 1 2 = 0.5 Since the difference between consecutive terms is constant (0.5 or 1/2), the sequence is an AP with a common difference d = 1 2 . Next three terms: a 5 = 7/2 + 1/2 = 4 a 6 = 4 + 1/2 = 9/2 a 7 = 9/2 + 1/2 = 5 Result: The sequence is an AP with common difference d = 1 2 . The...

NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.1 Question 4 (i) Question: Which of the following are APs ? If they form an AP, find the common difference d and write three more terms. 2, 4, 8, 16, . . . Given: The sequence: 2, 4, 8, 16, . . . To Find: Whether the given sequence is an AP. If it is an AP, find the common difference (d) and the next three terms. Formula: In an Arithmetic Progression (AP), the difference between consecutive terms is constant. This constant difference is called the common difference (d). Solution: Let's find the differences between consecutive terms: 4 - 2 = 2 8 - 4 = 4 16 - 8 = 8 Since the differences between consecutive terms are not constant, the given sequence is not an arithmetic progression (AP). Result: The sequence 2, 4, 8, 16, ... is not an AP. Next question solution: NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.1 Question 4 (ii). Explore more in Arithmetic Progress...

NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.1 Question 2 (iv) Question: Write first four terms of the AP, when the first term a and the common difference d are given as follows: a=–1, d=1/2. Given: First term (a) = –1 Common difference (d) = 1 2 To Find: First four terms of the AP Formula: n th term of an AP = a + (n-1)d Solution: First term (a 1 ) = a = –1 Second term (a 2 ) = a + d = –1 + 1 2 = -1 1 + 1 2 = -2+1 2 = -1 2 = - 1 2 Third term (a 3 ) = a + 2d = –1 + 2( 1 2 ) = –1 + 1 = 0 Fourth term (a 4 ) = a + 3d = –1 + 3( 1 2 ) = –1 + 3 2 = –1 + 1.5 = 0.5 = 1 2 Result: The first four terms of the AP are –1, – 1 2 , 0, 1 2 Next question solution: NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.1 Question 2 (v). Explore more in Arithmetic Progressions chapter: Click this link to explore more NCERT Class X Chapter 5 Arithmetic Progressions solutions Explore more: Click this link to ...