Question

Consider the following series: 50 + -10 + 2 + ... what is the sum of the first 5 terms?

Answer 1

`1024/25` or `41.68`

Explanation:

This series looks like a geometric progression(GP) with a common ratio of `-1/5`. A geometric progression is a series of the form `a,a*r,a*r^2,...` where ‘r’ is called the common ratio.The formula for the sum of a geometric series is `a*(r^n-1)/(r-1)` where ‘a’ is the first term, ‘r’ is the common ratio and ‘n’ is the number of terms. Substituting the values from the given series, we get `50*(((-1/5)^5)-1)/((-1/5)-1`

This simplifies into `1024/ 25` or 41.68