Chapter 8.2, Problem 26PPS

To determine

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

  $3,8,13,\mathrm{18...};$ 20^th term.

Answer to Problem 26PPS

The equation that describes the sequence is $t=5n-2$ and the 20^th term is 98.

Explanation of Solution

Given information:

Term number (n)	1	2	3	4
Term (t)	3	8	13	18

Calculation:

The terms have a common difference of 5. The term is 2 less than five times the term number. So the equation that describes the sequence is $t=5n-2$

Use the equation to find the 20^th term. Let. $n=20$

  $t=5n-2$

Write the equation

  $t=\left(5\times 20\right)-2$

Substitute the value of n i.e. 20

  $t=100-2$

Multiply 5 and 20 first i.e.100

  $t=98$

Subtract 2 from 100 i.e. 98

Thus the 20^th term is 98.