Very-Short and Short-Answer Questions


Very-Short and Short-Answer Questions

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


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

$\therefore S_{m}=2 m^{2}+3 m$

$\Rightarrow S_{m-1}=2(m-1)^{2}+3(m-1)=2\left(m^{2}-2 m+1\right)+3(m-1)=2 m^{2}-m-1$


$m^{\text {th }}$ term of the AP, $a_{m}=S_{m}-S_{m-1}$

$\therefore a_{m}=\left(2 m^{2}+3 m\right)-\left(2 m^{2}-m-1\right)=4 m+1$

Putting m = 2, we get

$a_{2}=4 \times 2+1=9$

Hence, the second term of the AP is 9.


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