Chapter 8.2, Problem 19PPS

To determine

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

  $16,17,18,\mathrm{19...};23rd$ term.

Answer to Problem 19PPS

The equation that describes the sequence is $t=n+15$ and the 23^rd term is 38.

Explanation of Solution

Given information:

Term number (n)	1	2	3	4
Term (t)	16	17	18	19

Calculation:

The terms have a common difference of 1. The term is 15 more than the term number. So the equation that describes the sequence is $t=n+15$

Use the equation to find the 23^rd term. Let $n=23.$

  $t=n+15$

Write the equation

  $t=23+15$

Substitute the value of n i.e. 23

  $t=38$

Add 23 and 15 i.e. 38

Thus the 23^rd term is 38.