Question

if the nth term of an AP is 3 + 2n, then sum of first 10 terms is ____________​

Answer 1

$Given \: n^{th} \: term \: of \: A.P: \\ (a_{n}) = 3+2n$

$First \: term (a_{1})\\ = 3 + 2 \times 1 \\= 3 + 2 \\= 5$

$10^{th} \: term (a_{10})\\ = 3 + 2 \times 10\\= 3 + 20 \\= 23$

$\boxed{ \pink{Sum \: of \: n \: terms\:( S_{n}) = \frac{n}{2}( a_{1} + a_{n}) }}$

$Here , a_{1} = 5, a_{10} = 23 \: and \: n = 10$

$Sum \: of \: 10 \:terms \: S_{10} \\= \frac{10}{2}( 5+23) \\= 5 \times 28 \\= 140$

Therefore.,

$\red{ Sum \: of \: 10 \:terms}\green { = 140}$

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