Chapter 7.8, Problem 50PPE

To determine

To calculate:Equation for the equation.

Answer to Problem 50PPE

The sequence is $4,8,16,32,64,\mathrm{.....}$

Explanation of Solution

Given information:

First day rehearse for 4 times a day

doubles the number of times each day

Formula used:

Recursive formula:

  $a_n=a_{n-1}\cdot r$

Explicit formula:

  $a_n=a\cdot r^{n-1}$

Calculation: 

As the rehearsal is doubles up each day so it is a geometric sequence for which r=2

And a=4

So explicit formula is

  $\begin{array}{l}{a}_n=a\cdot r^{n-1}\\ a_n=4\cdot 2^{n-1}\end{array}$

And the recursive formula is

  $\begin{array}{l}{a}_n=a_{n-1}\cdot r\\ a_n=a_{n-1}\cdot 2\\ a_n=2a_{n-1}\end{array}$

So the sequence is $4,8,16,32,64,\mathrm{.....}$