Question

The sum of first 'n' terms of the series a, 3a, 5a,...

Answer 1

Answer:

$an^{2}$

Step-by-step explanation:

Here, first term = a

second term = 3a

so, common difference(d)  = second term - first term

= 3a - a =  +2a

Now, by the 'sum of n terms formula'

$s_{n}$  = $\frac{n}{2}(2a +(n-1)d))$

substituting a = a, d = 2a, we get

$s_{n}$  = $\frac{n}{2}(2a +(n-1)(2a)))$

                         =$\frac{n}{2}(2a + 2an - 2a))$

                         =$\frac{n}{2}(2an))$

                         = (n)(an) = $an^{2}$

So, sum of n terms is $an^{2}$.