Chapter 8, Problem 22CR

To determine

To find: the first five terms of the arithmetic sequence and verify the result using calculator.

Answer to Problem 22CR

First five terms of an arithmetic sequence is $\underset{\_}{8,6,4,2,0}$ .

Explanation of Solution

Given information:

First term of the arithmetic sequence that is $a_1=8$ .

Common difference of arithmetic sequence is $d=-2$ .

Formula used:

nth term of an arithmetic sequence that is $a_n=a_1+\left(n-1\right)d$ where $a_1$ is first term and $d$ is common difference .

Calculation:

First term of the arithmetic sequence that is $a_1=8$ .

Common difference of arithmetic sequence is $d=-2$ .

Substitute $a_1=8$ and $d=-2$ in $a_n=a_1+\left(n-1\right)d$

  $a_n=8+\left(n-1\right)(-2)$

  $=8-2n+2$

  $=10-2n$

For first term of sequence $n=1$ that is $a_1=10-2(1)=10-2=8$ .

For second term of sequence $n=2$ that is $a_2=10-2(2)=10-4=6$ .

For third term of sequence $n=3$ that is $a_3=10-2(3)=10-6=4$ .

For fourth term of sequence $n=4$ that is $a_4=10-2(4)=10-8=2$ .

For fifth term of sequence $n=5$ that is $a_5=10-2(5)=10-10=0$ .

Verification of five terms using utility.

  

Hence first five terms of an arithmetic sequence is $\underset{\_}{8,6,4,2,0}$ .