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

Let first term of A.P. be a.

Given,

Common difference (d) = 7

By formula,

a_n = a + (n - 1)d

Given,

⇒ a₂₂ = 149

⇒ a + 7(22 - 1) = 149

⇒ a + 7 × 21 = 149

⇒ a + 147 = 149

⇒ a = 149 - 147 = 2.

Last term (l) = 22nd term = 149

By formula,

Sum of A.P. (S) = $\dfrac{n}{2}(a + l)$

Substituting values we get :

$\text{Sum of first 22 terms} = \dfrac{22}{2}(2 + 149) \\[1em] = 11 \times 151 \\[1em] = 1661.$

Hence, sum of first 22 terms = 1661.