Question

Find the sum of first 22 terms of an AP in which d = 7 and 22nd term is 149.

NCERT Class X
Mathematics - Mathematics

Chapter _ARITHMETIC PROGRESSIONS

Answer 1

Given,

$22^{nd}$ term in the A.P = 149.

Common difference d= 7.

To Find,

The first 22terms sum.

Solution,

Given that,

$22^{nd}$ term in the given A.P is 149.

And 7 is the difference between the terms in the A.P.

First, need to find the first number in the A.P

aₙ = a +(n-1)d.

a₂₂ = a+(n-1)d.

149 = a+(22-1)7

a = 149-147

a = 2.

2 is the first number in the A.P.

Let's find the total of the first 22terms.

Sₙ = $\frac{n}{2}$(a₁+a₂₂).

Sₙ = $\frac{22}{2}$(2+149)

Sₙ= 11×151

Sₙ = 1661.

Hence, 1661 is the sum of the first 22 numbers in the A.P.