NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.2 Question 18
NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.2 Question 18
Question:
The sum of the 4th and 8th terms of an AP is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of the AP.
Given:
Sum of 4th and 8th terms = 24
Sum of 6th and 10th terms = 44
To Find:
First three terms of the AP
Formula:
nth term of an AP = a + (n-1)d, where
'a' is the first term and
'd' is the common difference.
Solution:
Let the first term be 'a' and the common difference be 'd'.
4th term = a + 3d
8th term = a + 7d
Sum = (a + 3d) + (a + 7d) = 2a + 10d = 24
⇒ a + 5d = 12
6th term = a + 5d
10th term = a + 9d
Sum = (a + 5d) + (a + 9d) = 2a + 14d = 44
⇒ a + 7d = 22
Subtracting the first equation from the second:
(a + 7d) - (a + 5d) = 22 - 12
⇒ 2d = 10
⇒ d = 5
Substituting d = 5 in a + 5d = 12
⇒ a + 5(5) = 12
⇒ a = 12 - 25 = -13
First term (a1) = a = -13
Second term (a2) = a + d = -13 + 5 = -8
Third term (a3) = a + 2d = -13 + 10 = -3
Result:
The first three terms of the AP are -13, -8, -3.
Next question solution:
NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.2 Question 19
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