Question

If the sum of the first n terms of a series be 5n² + 2n, then its second term is (a) 56/15 (b) 27/14 (c) 17 (d) 16

Answer 1

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

$\green{\tt{\therefore{Second\:term=17}}}$

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

$\green{\underline \bold{Given: }} \\ \tt: \implies Sum \: of \: n \: terms = {5n}^{2} + 2n \\ \\ \red{\underline \bold{To \: Find: }} \\ \tt: \implies Second \: term( a_{2}) = ?$

• According to given question :

$\tt: {\implies {5n}^{2} + 2n} \\ \\ \tt \circ \: n = 1,2,3,4,... \\ \\ \bold{As \: we \: know \:that} \\ \tt: \implies s_{1} = 5 \times {1}^{2} + 2 \times 1 \\ \\ \tt: \implies s_{1} =5 + 2 \\ \\ \green{\tt: \implies s_{1} =7 = a_{1}} \\ \\ \bold{For \: s_{2} : } \\ \tt: \implies s_{2} = 5 \times {2}^{2} + 2 \times 2 \\ \\ \tt: \implies s_{2} =5 \times 4 + 4 \\ \\ \green{\tt: \implies s_{2} =24} \\ \\ \bold{For \: a_{2} : } \\ \tt: \implies a_{2} = s_{2} - s_{1} \\ \\ \tt: \implies a_{2} = 24 - 7 \\ \\ \green{\tt: \implies a_{2} = 17}$

Answer 2

Answer:

$\bf{\dag}\:\:\boxed{\sf S_n = 5n^2+2n}$

$\rule{100}{1}$

$\underline{\bigstar\:\textsf{First Term of AP :}}$

$\implies\tt S_1=5(1)^2+2(1)\\\\\\:\implies\tt S_1=5 \times 1 + 2\\\\\\:\implies\tt S_1 = 5 + 2\\\\\\:\implies\tt S_1 = 7 = a_1$

$\rule{200}{2}$

$\underline{\bigstar\:\textsf{Second Term of AP :}}$

$\dashrightarrow\tt\:\:a_2=S_2-S_1\\\\\\\dashrightarrow\tt\:\:a_2=(5n^2+2n)-7\\\\\\\dashrightarrow\tt\:\:a_2=[5(2)^2+2(2)]-7\\\\\\\dashrightarrow\tt\:\:a_2=[5\times4 + 4]-7\\\\\\\dashrightarrow\tt\:\:a_2=[20+4]-7\\\\\\\dashrightarrow\tt\:\:a_2=24-7\\\\\\\dashrightarrow\:\:\underline{\boxed{\red{\tt a_2=17}}}$

⠀

$\therefore\:\underline{\textsf{Second Term of AP will be c) \textbf{17}}.}$