Question

if the sum of first k terms of an ap is 2k+3k, then find the 2nd term​

Answer 1

CORRECT QUESTION :

If the sum of first k terms of an ap is 2k^2+3k, then find the 2nd term.

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Second\:term=9}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies Sum \: of \: k \: term \: of \: A.P = 2k^{2} + 3k\\ \\ \red{\underline \bold{To \: Find:}} \\ \tt: \implies Second \: term = ?$

• According to given question :

$\tt \circ \: s_{n} =2k^{2} + 3k \\ \\ \tt \because \: n = 1,2,3,....\\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies s_{1} = 2 \times {1}^{2} + 3 \times 1 \\ \\ \tt: \implies s_{1} = 2 + 3 \\ \\ \green{\tt: \implies s_{1} = 5 = a_{1}} \\ \\ \bold{For \: s_{2} \: (n = 2) : } \\ \tt: \implies s_{2} = 2 \times {2}^{2} + 3 \times 2 \\ \\ \tt: \implies s_{2} = 8 + 6 \\ \\ \green{\tt: \implies s_{2} = 14} \\ \\ \bold{For \: a_{2}} \\ \tt: \implies a_{2} = s_{2} - s_{1} \\ \\ \tt: \implies a_{2} =14 - 5\\ \\ \green{\tt: \implies a_{2} = 9}$

Answer 2

$\tt{\huge{\green{Hello!!! }}}$

Question :

If the sum of first k terms of an ap is 2k+3k, then find the 2nd term.

Solution :

$\tt{\red{Given\: - }}$

$\tt{\purple{\leadsto{S_{k} = 2{k}^2 + 3k }}}$

$\tt{\blue{\leadsto{S_{1} = 2{1}^2 + 3 = 5 }}}$

$\tt{\orange{\leadsto{S_{2} = 2{2}^2 + 6 = 14 }}}$

$\tt{\purple{\mapsto{a = 5 }}}$

$\tt{\pink{\mapsto{d = 9 }}}$

Hence ,

$\tt{ \orange{ \mapsto{A.P. = > 5 \:, \: 14, \: 23, \: }}}........(A)$