Question

Evaluate the series: 2-10+50-250..., n=8

Answer 1

The sum of first 8 terms of series is -130208

Solution:

Given that,

2 - 10 + 50 - 250 , ....

n = 8

Find the common ratio between a term and its previous term

$r = \frac{-10}{2} = -5\\\\r = \frac{-250}{50} = -5$

Thus common ratio is same

This is a geometric series

The sum of terms of geometric sequence is given as:

$S_n = \frac{a_1(1-r^n)}{1-r}$

Where,

r is the common ratio

n is the nth term

$a_1$ is the first term of series

From series,

$a_1 = 2\\\\r = -5\\\\n = 8$

Therefore,

$S_8 = \frac{2 \times (1 - (-5)^8)}{1-(-5)}\\\\S_8 = \frac{2 \times (1-390625)}{6}\\\\S_8 = -130208$

Thus sum of first 8 terms of series is -130208