Question

Find the $n^{th}$ term of the series 3.4.7 + 4.5.9 + 5.6.11 + -------------

• A. (2n + 1) (2n + 2) (3n + 1)
• B. (n+2) (n+3) (n + 5)
• C. (n+2) (n+3) (2n + 5)
• D. (2n +1) (n + 3) (3n + 5)

Answer 1

The correct option is C

(n+2) (n+3) (2n + 5)

We see that each terms having the multiplication of 3 different Arithmetic progressions.

So,$n^{th}$ term of series is multiplication of $n^{th}$ terms of different APs.

$n^{th}$Term is $t_n$ = (n + 2) (n + 3) (2n + 5)