Chapter 4.7, Problem 31P

Find the third, fifth, and tenth terms of the sequence described by each explicit formula.

$A(n)=2.5+(n-1)(2.5)$

To determine

To find:The value of third, fifth and tenth term.

Answer to Problem 31P

The value of third, fifth and tenth term is 7.5, 12.5 and 25

Explanation of Solution

Given:

  $A\left(n\right)=2.5+\left(n-1\right)\left(2.5\right)$

Calculation:

Calculate the third term.

  $\begin{array}{c}A\left(3\right)=2.5+\left(3-1\right)\left(2.5\right)\\ =2.5+2\left(2.5\right)\\ =7.5\end{array}$

Calculate the fifth term.

  $\begin{array}{c}A\left(5\right)=2.5+\left(5-1\right)\left(2.5\right)\\ =2.5+4\left(2.5\right)\\ =12.5\end{array}$

Calculate the tenth term.

  $\begin{array}{c}A\left(10\right)=2.5+\left(10-1\right)\left(2.5\right)\\ =2.5+9\left(2.5\right)\\ =25\end{array}$

Thus, the value of third, fifth and tenth term is 7.5, 12.5 and 25