Find the sum of first 22 terms of an AP in which d = 7 and \(22^{nd}\) term is 149.

Given,
Common difference, d = 7
\(22^{nd}\) term, \(a_{22}\) = 149

We have to find the sum of first 22 term, \(S_{22}\)
By the formula of nth term,

\(\Rightarrow a_n = a + (n - 1)d\)
\(\Rightarrow a_{22} = a + (22 - 1)d\)
\(\Rightarrow \) 149 = a + (21)(7)
\(\Rightarrow \) 149 = a + 147
\(\Rightarrow \) a = 2 = First term

Sum of n terms,

\(\Rightarrow S_n = {{n} \over {2}}(a+a_n)\) = \({{22} \over {2}}\) (2+149) = 11×151 = 1661