Question

Find the sum of the arithmetic series.
20
(Sigma Sign) 2n + 7
x= 1
Formula: Sn= a1 (1 - r^n / 1 - r)

Answer 1

The formula you wrote down is applicable for geometric series. I would suggest that you study the derivations of the formulae for arithmetic and geometric series. It's no use compute the answers using formulae that you don't understand.

In case of this problem:

Summation of 2n + 7 =

2 [Summation of n] + 7 [summation of 1]

Summation of n from 1 to 20 =

1/2 Summation of n from 1 to 20 +

1/2 Summation of n from 1 to 20 =

1/2 Summation of n from 1 to 20 +

1/2 Summation of n from 20 to 1 =

1/2 Summation of n from 1 to 20 +

1/2 Summation of (21 - n) from 1 to 20 =

1/2 Summation of 21 from 1 to 20 =

1/2 21*20

So, the summation is 21*20 + 7*20 =28*20 = 560