Question

Find the sum of first 20terms of an ap in which the first term is 1and common difference is 3

Answer 1

Answer:-

$\sf{The \ sum \ of \ first \ 20 \ terms \ is \ 590.}$

Given:

• In an Ap,

1. First term(a)=1
2. Common difference(d)=3

To find:

• Sum of first 20 terms.

Solution:

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

$\sf{\therefore{S_{20}=\frac{20}{2}[2(1)+(20-1)\times3]}}$

$\sf{\therefore{S_{20}=10[2+19(3)]}}$

$\sf{\therefore{S_{20}=10[2+57]}}$

$\sf{\therefore{S_{20}=10\times59}}$

$\sf{\therefore{S_{20}=590}}$

$\sf\purple{\tt{\therefore{The \ sum \ of \ first \ 20 \ terms \ is \ 590.}}}$

Answer 2

Given ,

First term (a) = 1

Common difference (d) = 3

We know that ,

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

Thus ,

$\sf \mapsto S_{20} = \frac{20}{2} (2 \times 1 + (20 - 1)3) \\ \\ \sf \mapsto S_{20} =10(2 + 57) \\ \\ \sf \mapsto S_{20} =590$

$\sf \therefore \underline{The \: sum \: of \: first \: 20 \: terms \: of \: AP \: is \: 590 \: }$