The sum of the 4^th and 8^th terms of an AP is 24 and the sum of the 6^th and 10^th terms is 44. Find the first three terms of the AP.

Solution:

The formula for n^th term of an AP is aₙ = a + (n - 1) d

Here, aₙ is the n^th term, a is the first term, d is the common difference and n is the number of terms.

Given, a₄ + a₈ = 24

(a + 3d) + (a + 7d) = 24

⇒ 2a + 10d = 24

⇒ a + 5d = 12  ..... Equation(1)

Also, a₆ + a₁₀ = 44

(a + 5d ) + (a + 9d) = 44

⇒ 2a + 14d = 44

⇒ a + 7d = 22 .... Equation(2)

On subtracting equation (1) from (2), we obtain

(a + 7d ) - (a + 5d) = 22 - 12

a + 7d - a - 5d = 10

2d = 10

d = 5

By substituting the value of d = 5 in equation (1), we obtain

a + 5d = 12

a + 5 × 5 = 12

a + 25 = 12

a = - 13

The first three terms are a , (a + d) and (a + 2d)

Substituting the values of a and d , we get - 13, (- 13 + 5) and (- 13 + 2 × 5) 

The first three terms of this A.P. are - 13, - 8, and - 3.

☛ Check: NCERT Solutions for Class 10 Maths Chapter 5

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Video Solution:

The sum of the 4^th and 8^th terms of an AP is 24 and the sum of the 6^th and 10^th terms is 44. Find the first three terms of the AP.

Class 10 Maths NCERT Solutions Chapter 5 Exercise 5.2 Question 18

Summary:

The sum of the 4^th and 8^th terms of an AP is 24 and the sum of the 6^th and 10^th terms is 44. The first three terms of the AP are - 13, - 8, and - 3.

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