Question

What is the sum of the first seven terms of the geometric series 2 - 10 +50 -...?

Answer 1

26042.

Explanation:

What's the first term of this geometric series?

2.

What's the common ratio of this geometric series?

Divide one of the terms with the previous term. For example, divide the second term -10 with the first term 2.

`\displaystyle r = (-10)/(2) = -5`.

What's the sum of this series to the seventh term?

The sum of the first n terms of a geometric series is:

`\displaystyle a_1 \cdot (1-r^(n))/(1-r)`,

where

• 
  `a_1` is the first term of the series,
• 
  `r` is the common ratio of the series, and
• 
  `n` is the number of terms in this series.

`\displaystyle 2 *(1- (-5)^(7))/(1- (-5))=26,042`.