Chapter 12.3, Problem 25AYU

To determine

To find: The seventh term of the geometric sequence.

Answer to Problem 25AYU

The seventh term of the sequence is $\frac{1}{64}$ .

Explanation of Solution

Given information:

The sequence is $1,\frac{1}{2},\frac{1}{4}\mathrm{.......}$ .

Calculation:

The first term of a sequence is denoted as $a_1$ and the second term of the sequence is denoted by $a_2$ .

Calculate the common ratio.

  $\begin{array}{c}r=\frac{a_2}{a_1}\\ =\frac{\frac{1}{2}}{1}\\ =\frac{1}{2}\end{array}$

The formula for nth term of geometric sequence is given by,

  $a_n=a_1{r}^{n-1}$

Calculate the fifth term.

  $\begin{array}{c}{a}_7=\left(1\right){\left(\frac{1}{2}\right)}^{7-1}\\ =\left(1\right){\left(\frac{1}{2}\right)}^6\\ =\frac{1}{64}\end{array}$

Therefore, the seventh term of the sequence is $\frac{1}{64}$ .