Question

True or False: For a geometric sequence with first term$a_1$ and common ratio$r$where$r\ne 0$,$r\ne 1$the sum of the first$n$terms isrole="math" localid="1646843821067" $s_n=a_1\frac{1-r^n}{1-r}$.

Short answer

For a geometric sequence with first term $a_1$and common ratio $r$where $r\ne 0,r\ne 1$the sum of the first $n$terms isrole="math" localid="1646844482598" $s_n=a_1\frac{1-r^n}{1-r}$is true.

Step-by-step solution

Step 1. Given information.

True or False For a geometric sequence with first term $a_1$and common ratio $r$where, $r\ne 0r,\ne 1$the sum of the first $n$terms is $s_n=a_1\frac{1-r^n}{1-r}$

• A geometric progression, also known as a geometric sequence, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

Step 2. True or false.

The given statement is true.