Question

question 30 find the sum of the following geometric series: 10+6+3.6+2.16+... 25 22 20 16

Explanation:

Step1: Identify the first term and common ratio

The first term \( a = 10 \). The common ratio \( r \) is found by dividing the second term by the first term: \( r=\frac{6}{10} = 0.6 \). Since \( |r|=0.6<1 \), the sum of an infinite geometric series formula \( S=\frac{a}{1 - r} \) applies.

Step2: Apply the infinite geometric series formula

Substitute \( a = 10 \) and \( r = 0.6 \) into the formula: \( S=\frac{10}{1 - 0.6} \).

Step3: Calculate the denominator and then the sum

First, calculate the denominator: \( 1 - 0.6=0.4 \). Then, \( S=\frac{10}{0.4}=25 \).

Answer:

25