Question

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

Answer 1

\(d = 7\), \(a_{22} = 149\), \(S_{22 }=?\)
\(a_n = a + (n − 1)d\)
\(a_{22} = a + (22 − 1)d\)
\(149 = a + 21 × 7\)
\(149 = a + 147\)
\(a = 2\)
\(S_n = \frac n2[a + a_n]\)

\(S_{22} = \frac {22}{2 }[2 + 149]\)
\(S_{22}= 11 \times  151\)
\(S_{22}= 1661\)