Question

Consider the arithmetic series:

Answer 1

The sum of an Arithmetic Series is given as:

$S_{n}= \frac{n}{2}(2a_{1}(n-1)*d)$

where,
d = Common Difference = Difference of any two consecutive terms.
So,
d = 8

a1 = First term = 1

Using the values, we get:

$S_{n}= \frac{n}{2}(2*1+(n-1)*8) \\ \\ S_{n}= \frac{n}{2} (2+8n-8) \\ \\ S_{n}= \frac{n}{2}(8n-6) \\ \\ S_{n}=n(4n-3) \\ \\ S_{n}==4n^{2}-3n$

The above equation gives the formula for n terms of an Arithmetic Series.

So, option A is the correct answer