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

Solution:

Given,

Common difference, d = 7

22^nd term, a₂₂ = 149

The sum of the first 22 terms, S₂₂ = ?

By the formula of the nth term,

a_n = a + (n − 1) d

a₂₂ = a + (22 − 1) d

149 = a + 21 × 7

149 = a + 147

a = 2 = First term

The sum of n terms,

S_n = n /2( a + a_n )

S₂₂ = 22/2 (2 + 149)

= 11 × 151

= 1661