Chapter 8.2, Problem 20PPS

To determine

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

  $14,15,16,\mathrm{17...};16th$ term.

Answer to Problem 20PPS

The equation that describes the sequence is $t=n+13$ and the 16^th term is 29.

Explanation of Solution

Given information:

Term number (n)	1	2	3	4
Term (t)	14	15	16	17

Calculation:

The terms have a common difference of 1. The term is 13 more than the term number. So the equation that describes the sequence is $t=n+13$

Use the equation to find the 16^th term. Let $n=16$

  $t=n+13$

Write the equation

  $t=16+13$

Substitute the value of n i.e. 16

  $t=29$

Add 23 and 15 i.e. 29

Thus the 16^th term is 29.