Question

6. Find the sum of the first 22 terms of an
A.P. whose first term is 4 and the common
difference is 4/3 *
(2 Points)​

Answer 1

Given ,

First term (a) = 4

Common difference (d) = 4/3

We know that , the sum of first n terms of an AP is given by

$\boxed{ \sf{S_{n} = \frac{n}{2} \{ 2a + (n - 1)d\}}}$

Thus ,

$\sf \mapsto S_{22} = \frac{22}{2} \{2 \times 4 + (22 - 1) \frac{4}{3} \}11 \times (8 + 28) \\ \\\sf \mapsto S_{22} = 11 \times 36 \\ \\\sf \mapsto S_{22} = 396$

$\sf \therefore \underline{The \: sum \: of \: first \: 22 \: terms \: of \: given \: AP \: is \: 396}$