Question

The sum of first $p$-terms of a sequence is $p(p+1)(p+2)$. The ${10}^{th}$ term of the sequence is

• A. $396$
• B. $600$
• C. $330$
• D. $114$

Answer 1

The correct option is C $330$

Given,

$S_p=p(p+1)(p+2)$

$\Rightarrow S_p=p^3+3p^2+2p$

and

$S_{p-1}=(p-1)\left(p\right)(p+1)$

$\Rightarrow S_{p-1}=p^3-p$

Now, pth term,

$a_p=S_p-S_{p-1}$

$=p^3+3p^2+2p-(p^3-p)$

$\therefore a_p=3p^2+3p$

Now,

$a_{10}=3(10{)}^2+3(10)$

$=300+30$

$=330$