Question

If sum of first n terms of a series is $S_n=3n^3+2n^2$, then $6^{th}$ term is

• A. $309$
• B. $720$
• C. $101$
• D. $295$

Answer 1

Answer: (D)

$295$

$S_n=3n^3+2n^2\left(Given\right)$

$S_5=3{\left(5\right)}^3+2{\left(5\right)}^2=425$

$S_6=3{\left(6\right)}^3+2{\left(6\right)}^2=720$

As we know that,

$a_n=S_n-S_{n-1}$

Therefore,

$a_6=S_6-S_5$

$\Rightarrow a_6=720-425=295$