Question

What is the value of r in the geometric series 1.3(0.8)^(n-1) where the summation is from n = 1 to 3?

A) 0.8
B) 1.3
C) 3.0
D) 3.2

Answer 1

The common ratio (value of r) in the given geometric series 1.3(0.8)^(n-1) is 0.8, which is the factor that is repeatedly multiplied to each term to obtain the next term.

Step-by-step explanation:

To find the value of r in the geometric series given by 1.3(0.8)(n-1), where the summation is from n = 1 to 3, we need to substitute n = 1, 2, and 3 into the expression and add the terms together.

For n = 1: 1.3(0.8)(1-1) = 1.3(0.8)0 = 1.3 × 1 = 1.3

For n = 2: 1.3(0.8)(2-1) = 1.3(0.8)1 = 1.3 × 0.8 = 1.04

For n = 3: 1.3(0.8)(3-1) = 1.3(0.8)2 = 1.3 × 0.64 = 0.832

Summing these values: 1.3 + 1.04 + 0.832 = 3.172

However, the values given in the question for r do not match with the obtained sum. If the question is asking for the common ratio of the geometric series, then the common ratio r is 0.8, which is the factor by which each term is multiplied to get the next term in the series.