Question

Very-Short and Short-Answer Questions

If the sum of first m terms of an AP is (2m² + 3m) then what is its second term? [CBSE 2011]

Answer 1

Let S_m denotes the sum of first m terms of the AP.

$$\begin{gathered} \therefore S_m=2m^2+3m \\ \Rightarrow S_{m-1}=2{\left(m-1\right)}^2+3\left(m-1\right)=2\left(m^2-2m+1\right)+3\left(m-1\right)=2m^2-m-1 \end{gathered}$$
Now,
m^th term of the AP, a_m = S_m − S_{m − 1
$\therefore a_m=\left(2m^2+3m\right)-\left(2m^2-m-1\right)=4m+1$}
Putting m = 2, we get
$a_2=4\times 2+1=9$

Hence, the second term of the AP is 9.