Chapter 12.3, Problem 28AYU

In Problems 27-32, find the indicated term of each geometric sequence.

8th terms of $1,3,9,\dots$

To determine

To calculate: The value of the ${\text{8}}^{\text{th}}$ term of the geometric sequence $1,3,9,\cdots$.

Answer to Problem 28AYU

Solution:

The value of the $8^{\text{th}}$ term is $a_8=2187$.

Explanation of Solution

Given:

The sequence is given by $1,3,9,\cdots$.

The first term $a_1=1$ and the common ratio $r=\frac{a_n}{a_{n-1}}=\frac{a_2}{a_1}=\frac{a_3}{a_2}=\dots =3$.

Formula Used:

The $n^{\text{th}}$ term of the geometric sequence is given by,

$a_n=a_1\cdot r^{n-1}$

The $8^{\text{th}}$ term of the geometric sequence is given by $a_8=1\cdot {\left(3\right)}^{8-1}={\left(3\right)}^7=2187$.