Question

Find the nth term of the series

2.5 + 5.8 + 8.11 + ------------

• A. (n + 2) (n + 5)
• B. (2n + 1) (2n + 3)
• C. (3n - 1) (3n + 2)
• D. (4n - 2) (4n + 1)

Answer 1

The correct option is C

(3n - 1) (3n + 2)

Observe that 2, 5, 8, 11, - - - - are in A.P with 1st term = 2 and common difference = 3.

Also observe all the second numbers in each term i.e., 5, 8, 11, - - - - . They are in A.P with 5 as 1st term and 3 as common difference.

So, nth term of the given series,

$T_n$ = (nth term of 2, 5, 8, .........).(nth term of 5, 8,11, .........)

= [2+(n-1)3][5+(n-1)3]

= (3n - 1) (3n + 2)