Chapter 8.2, Problem 23PPS

To determine

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

  $7,10,13,\mathrm{16...};$ 20^th term.

Answer to Problem 23PPS

The equation that describes the sequence is $t=3n+4$ and the 20^th term is 64.

Explanation of Solution

Given information:

Term number (n)	1	2	3	4
Term (t)	7	10	13	16

Calculation:

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

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

  $t=3n+4$

Write the equation

  $t=\left(3\times 20\right)+4$

Substitute the value of n i.e. 20

  $t=60+4$

Multiply 20 and 3 first i.e.60

  $t=64$

Add 60 and 4 i.e.64

Thus the 20^th term is 64.