Chapter 4.7, Problem 34P

Tell whether each sequence is arithmetic. Justify your answer. If the sequence is arithmetic, write a recursive and an explicit formula to represent it.

$5,13,21,29,\dots$

To determine

To find:Whether the given series is arithmetic or not and write the formula to represent it.

Answer to Problem 34P

The given sequence is arithmetic and the formula is $A\left(n\right)=5+\left(n-1\right)\left(8\right)$

Explanation of Solution

Given:

The given series is $5,13,21,29,\mathrm{...}$

Calculation:

Calculate the common difference.

  $\begin{array}{l}13-5=8\\ 21-13=8\\ 29-21=8\end{array}$

Thus, the common difference it 8 so, the sequence is arithmetic.

Write the formula to represent the equation.

  $A\left(n\right)=A\left(1\right)+\left(n-1\right)d$

Substitute the values in the above equation.

  $A\left(n\right)=5+\left(n-1\right)\left(8\right)$

Thus, the given sequence is arithmetic and the formula is $A\left(n\right)=5+\left(n-1\right)\left(8\right)$