Chapter 9.2, Problem 82E

To determine

To find: The two ways to calculate ${13}^{th}$ term.

Answer to Problem 82E

  $a_n=a_1+\left(n-1\right)d$

Explanation of Solution

Given information:

The first way is to use the common difference $d$ as $a_{13}=a+12d$ and the second way is to use $a_n=a_1+\left(n-1\right)d$ to find the $13\text{th}$ term.

Calculation:

The general method to find the $n^{th}$ term of an arithmetic sequence,

Consider the sequence $a_1,a_2$ as first and second term, find common difference as,

  $d=a_2-a_1$

The common difference can be added 12 times to the first term to find the 13th term of the sequence as,

  $a_{13}=a+12d$

The second way to obtain the 13^th term is by the use of arithmetic sequence formula,.

  $a_n=a_1+\left(n-1\right)d$

Here, $n$ is the number of term.

Hence, the first way is to use the common difference $d$ as $a_{13}=a+12d$ and the second way is to use $a_n=a_1+\left(n-1\right)d$ to find the $13\text{th}$ term.