Question

In an=2n+3 then the value of S3 is

Answer 1

Just insert the formula and with the help of Formula of Sum of N terms, find the Answer.

Answer 2

AnswEr :

☯ $\underline{\textsf{As \: per \: given \: in \: question:}}$

$\normalsize\ : \implies\sf\ a_{n} = 2n + 3$

$\scriptsize\sf{\quad\dag\ Let \: the \: value \: of \: n \: be \: 1}$

$\normalsize\ : \implies\sf\ a_{1} = 2 \times\ 1 + 3$

$\normalsize\ : \implies{\boxed{\sf \blue{a_{1} = 5}}}$

$\scriptsize\sf{\quad\dag\ Let \: the \: value \: of \: n \: be \: 2}$

$\normalsize\ : \implies\sf\ a_{2} = 2 \times\ 2 + 3$

$\normalsize\ : \implies{\boxed{\sf \pink{a_{2} = 7}}}$

$\rule{170}1$

$\underline{\bigstar\:\sf{From \: the \: Value \: of \: a_{2}\: \: and \: a_{1}:}}$

$\normalsize\dashrightarrow\sf\ Common \: difference(d) = a_{2} - a_{1}$

$\normalsize\dashrightarrow\sf\ d = 7 - 5$

$\normalsize\dashrightarrow{\boxed{\sf \red{ d = 2}}}$

$\underline{\bigstar\:\sf{Value \: of \: S_{3} :}}$

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

$\normalsize\dashrightarrow\sf\ S_{3} = \frac{3}{2} \left[ 2 \times\ 5 + ( 3 - 1)2 \right]$

$\normalsize\dashrightarrow\sf\ S_{3} = \frac{3}{2} \left[ 10 + (2)2 \right]$

$\normalsize\dashrightarrow\sf\ S_{3} = \frac{3}{2} \left[ 10 + 4 \right]$

$\normalsize\dashrightarrow\sf\ S_{3} = \frac{3}{\cancel{2}} \left[ \cancel{14} \right]$

$\normalsize\dashrightarrow\sf\ S_{3} = 21$

$\normalsize\dashrightarrow{\underline{\boxed{\sf \green{S_{3} = 21}}}}$