Question

In Problems 17–19, find the indicated term in each sequence.

11th term of $1,\frac{1}{10},\frac{1}{100},...........$

Short answer

11th term of the sequence is:$\frac{1}{{10}^{10}}$

Step-by-step solution

Step 1. Given information.

Sequence is$1,\frac{1}{10},\frac{1}{100},.......$

Step 2. To find type of sequence.

Since the ratio of two successive terms is constant.

Hence given sequence is a geometric sequence.

Its first term is $a_1=1$

Common ratio is $$\begin{gathered} r=\frac{1}{10}÷1 \\ =\frac{1}{10} \end{gathered}$$

Its 11th term is$$\begin{gathered} a_{11}=1.{\left(\frac{1}{10}\right)}^{11-1} \\ ={\left(\frac{1}{10}\right)}^{10} \end{gathered}$$