Question

Find the sum of the series : 3 + 5 + 7 + 6 + 9 + 12 + 9 + 13 + 17 + .... to 3n terms.

Answer 1

In the given series 3 + 5 + 7 + 9 + .... to 3n.
Here,
a = 3
d = 2
Number of terms = 3n
The sum of n term is
$S_n=\frac{n}{2}[2a+(n-1\left)d\right]\Rightarrow S_{3n}=\frac{3n}{2}[6+(3n-1\left)2\right]=3n(2n+3)$