Question

If sum of n terms of a sequence is given by $S_n=2n^2+3n$, Find it's ${10}^{th}$ term.

• A. 41
• B. 40
• C. 42
• D. 52

Answer 1

The correct option is A

41

In a sequence, we get the sum of n terms by adding $n^{th}$ term to the sum of (n-1)terms. We can write this as $S_n=S_{n-1}+t_n$

$\Rightarrow t_n=S_n-S(n-1)$
$=2n^2+3n-\left(2\right(n-1{)}^2+3(n-1))$
$=2n^2+3n-\left(2\right(n^2-2n+1)+3n-3)$
$=2n^2+3n-2n^2+4n-2-3n+3$
$=4n+1$
$\Rightarrow t_{10}=$ $4\times 10+1$
=41