Question

What is the sum of this arithmetic series?

Answer 1

Answer:

The sum of the arithmetic series

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

Step-by-step explanation:

Explanation

Let  a , a+d , a+2 d , ..........a+(n-1)d +....... is an arithmetic sequence

The sum of the sequence is called arithmetic series

The $n^{th}$ term of the sequence

$t_{n} = a + (n-1) d$

The sum of the arithmetic series

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

Here 'a' is the first term of the sequence

and 'd' be the difference between two values

sum of first term

put n=1  ⇒  $S_{1} = a$

Put n =2 ⇒ $S_{2} = \frac{2}{2} (2 a + (2-1)d)$

                  $S_{2} = 2 a + d$

......and so on

The sum of the  arithmetic series

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