NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.3 Question 5
NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.3 Question 5 Question: The first term of an AP is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference. Given: First term (a) = 5 Last term (l) = 45 Sum of the AP (S n ) = 400 To Find: Number of terms (n) and common difference (d) Formula: Sum of an AP: S n = n 2 (a + l) Last term of an AP: l = a + (n - 1)d Solution: Using the sum formula: 400 = n 2 (5 + 45) ⇒ 400 = 25n 1 ⇒ n = 16 Using the last term formula: 45 = 5 + (16 - 1)d ⇒ 40 = 15d ⇒ d = 40 15 ⇒ d = 8 3 ⇒ d = 2.5 Result: Number of terms (n) = 16 Common difference (d) = 2.5 Next question solution: NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.3 Question 6 Explore more in Arithmetic Progressions chapter: Click this link to explore more NCERT Class X Chapter 5 Arithmetic Progressions solutio...