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Answer :
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