Question

Write the sum using summation notation, assuming the suggested pattern continues. 5 - 15 + 45 - 135 + ...

summation of five times three to the power of the quantity n plus one from n equals zero to infinity
summation of five times negative three to the power of n from n equals zero to infinity
summation of five times three to the power of n from n equals zero to infinity
summation of five times negative three to the power of the quantity n plus one from n equals zero to infinity

Answer 1

summation of five times negative three to the power of n from n equals zero to infinity

Explanation:

Summation Notation

It represents the sum of a finite or infinite number of terms. Let's analyze the terms of the given succession:

5-15+45-135+...

If we take 5 as a common factor, we have

5(1-3+9-27+...)

The parentheses contain the alternate sum/subtraction of powers of 3. The odd terms are positive, the even terms are negative, thus the exponent must be n starting from 0 or n-1 starting from 1

The summation is then represented by

`\sum_(n=0)^(\infty)5(-3)^n`

This corresponds with the option:

summation of five times negative three to the power of n from n equals zero to infinity