Question

If the sum of first m terms of an AP is 2m^+3m then what is its second term?

Answer 1

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

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

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

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

• According to given question :

$\tt \circ \: s_{m} =2 {m}^{2} + 3m \\ \\ \tt \because \: m = 1,2,3,.... \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies s_{1} = {2 \times 1}^{2} + 3 \times 1 \\ \\ \tt: \implies s_{1} = 2 + 3 \\ \\ \green{\tt: \implies s_{1} = 5 = a_{1}} \\ \\ \bold{For \: s_{2}(n = 2)} \\ \tt: \implies s_{2} = 2 \times {2}^{2} + 3 \times 2 \\ \\ \tt: \implies s_{2} = 2 \times 4 + 6 \\ \\ \green{ \tt: \implies s_{2} = 14 }\\ \\ \bold{For \: second \: term : } \\ \tt: \implies a_{2} = s_{2} - s_{1} \\ \\ \tt: \implies a_{2} = 14 - 5 \\ \\ \green{\tt: \implies a_{2} = 9} \\ \\ \green{\tt \therefore Second \: term \: is \: 9}$

Answer 2

Given:-

Sum of first 'm' terms of an AP is 2m³+3m.

To find:-

The second term of the AP.

Solution:-

A/q,

$\bold{Sm=2m^2+m}$

We know,

Sm - S(m-1) = am

So, a2 = S2 - S1

a2 = $[2(2)^2+3*2]-[2(1)^2+3*1]$

⇒ a2 = $(8+6)-(2+3)$

⇒ a2 = $14-5$

$\boxed{\bold{a2=9}}$

∴Thus, the second term of the AP is 9.