Chapter 7.2, Problem 63MR

To determine

To Find: The third, seventh and tenth terms of the sequence described by the rule $A\left(n\right)=-5+\left(n-1\right)\left(2\right)$ .

Answer to Problem 63MR

The required third, seventh and tenth term of the sequence is -1, 5 and 13 respectively.

Explanation of Solution

Given information:

The sequence $A\left(n\right)=-5+\left(n-1\right)\left(2\right)$

Calculation:

  $A\left(n\right)=-5+\left(n-1\right)\left(2\right)$

To find the third term, substitute the term number as 3 i.e. $n=3$

  $A\left(3\right)=-5+\left(3-1\right)\left(2\right)$

(Substitute 3 for n)

  $\begin{array}{l}A\left(3\right)=-5+\left(2\right)\left(2\right)\\ A\left(3\right)=-5+4\\ A\left(3\right)=-1\end{array}$

(Simplify)

So, the third term is -1.

  $A\left(n\right)=-5+\left(n-1\right)\left(2\right)$

To find the seventh term, substitute the term number as 7 i.e. $n=7$

  $A\left(7\right)=-5+\left(7-1\right)\left(2\right)$

(Substitute 7 for n)

  $\begin{array}{l}A\left(7\right)=-5+\left(5\right)\left(2\right)\\ A\left(7\right)=-5+10\\ A\left(7\right)=5\end{array}$

(Simplify)

So, the seventh term is 5.

  $A\left(n\right)=-5+\left(n-1\right)\left(2\right)$

To find the tenth term, substitute the term number as 10 i.e. $n=10$ .

  $A\left(10\right)=-5+\left(10-1\right)\left(2\right)$

(Substitute 10 for n)

  $\begin{array}{l}A\left(10\right)=-5+\left(9\right)\left(2\right)\\ A\left(10\right)=-5+18\\ A\left(10\right)=13\end{array}$

(Simplify)

So, the tenth term is 13.