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

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

Thus common ratio is same

This is a geometric series

The sum of terms of geometric sequence is given as:

Where,

r is the common ratio

n is the nth term

is the first term of series

From series,

Therefore,

Thus sum of first 8 terms of series is -130208