Chapter 12.3, Problem 99AYU

To determine

To find: The 20^th term of the sequence.

Answer to Problem 99AYU

The 20^th term of the sequence is $a_{20}=524288\text{and}{a}_{20}^{/}=10485760$ .

Explanation of Solution

Given information:

Let, the sequences be $\begin{array}{l}\text{1, 2, 4,}\mathrm{............}\\ \text{20, 40, 80,}\mathrm{..........}\end{array}$

Calculation:

Calculate the value of $a_{20}$ .

Use formula: $a_n=a.r^{n-1}$

  $\begin{array}{c}{a}_{20}=a.r^{20-1}\\ $ =1{(2)}^{19}$=524288\end{array}$

Calculate the value of $a_{20}^{/}$

Use formula: $a_n=a.r^{n-1}$

  $\begin{array}{c}{a}_{20}^{/}=a.r^{20-1}\\ $ =20.{(2)}^{19}$=20\times 524288\\ =10485760\end{array}$

Therefore, the 20^th term of the sequence is $a_{20}=524288\text{and}{a}_{20}^{/}=10485760$ . $a_{20}=524288and{a}_{20}^{/}=10485760$ .