Chapter 8.2, Problem 25PPS

To determine

To Write: The equation for the given sequence and to find the indicated term.

  $1,5,9,\mathrm{13...};$ 89^th term.

Answer to Problem 25PPS

The equation that describes the sequence is $t=4n-3$ and the 89^th term is 353.

Explanation of Solution

Given information:

Term number (n)	1	2	3	4
Term (t)	1	5	9	13

Calculation:

The terms have a common difference of 4. The term is 3 less than four times the term number. So the equation that describes the sequence is $t=4n-3$

Use the equation to find the 89^th term. Let $n=89$ .

  $t=4n-3$

Write the equation

  $t=\left(4\times 89\right)-3$

Substitute the value of n i.e. 89

  $t=356-3$

Multiply 4 and 89 first i.e.356

  $t=353$

Subtract 3 from 356i.e. 353

Thus the 89^th term is 353.