Chapter 9.5, Problem 7LC

Solution

To explain how the formulas for the sum of finite arithmetic series and finite geometric series are similar and how they are different.

Given information:

The formulas for the finite arithmetic series and finite geometric series.

Explanation:

The formula for sum of the finite arithmetic sequence is given as $S_n=\frac{n}{2}\left(2a_1+\left(n-1\right)d\right)$ , where $a_1$ is the first term, $d$ is the common difference and $n$ is the number of terms in the series.

The formula for the sum of the finite geometric series is given as $S_n=\frac{a_1\left(1-r^n\right)}{1-r}$ , where $a_1$ is the first term, $r$ is the common ratio and $n$ is the number of terms in the series.

Observe that the both formulas use first term $a_1$ and the number of terms $n$ to find the sum of the series for the first $n$ terms.

The formulas are different in the sense that the formula for the sum of arithmetic series uses common difference and the formula for the sum of geometric series uses common ratio to calculate the sum.