Question

The $n ^ { t h }$ term of an A.P. is $3 n - 1$.Choose from the following the sum of its first five terms.

• A. 14
• B. 35
• C. 80
• D. 40

Answer 1

Answer: (D)

40

Answer 2

Here $T _ { n } = 3 n - 1$ , putting $n = 1,2,3,4,5$ we get first five terms, $2,5,8,11,14$

Hence sum is $2 + 5 + 8 + 11 + 14 = 40$ .

Aliter : $S _ { n } = \Sigma T _ { n } = 3 \Sigma n - \Sigma 1 = \frac { 3 n ( n + 1 ) } { 2 } - n$

$\Rightarrow$ $S _ { 5 } = \frac { 3.5 \cdot 6 } { 2 } - 5 = 40$ .