# 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

**Solution:**

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

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

Given, a_{4} + a_{8} = 24

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

⇒ 2a + 10d = 24

⇒ a + 5d = 12 ..... Equation(1)

Also, a_{6} + a_{10} = 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

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)

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

**Video Solution:**

## 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

### Class 10 Maths NCERT Solutions Chapter 5 Exercise 5.2 Question 18 - Chapter 5 Exercise 5.2 Question 18:

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

The first 3 terms of the A.P. are - 13, - 8, and - 3 if the sum of the 4th and 8th terms of an A.P. is 24 and the sum of the 6th and 10th terms is 44