Question

I can use the arithmetic sequence formula to find the nth term.I can write an arithmetic sequence equation to represent an arithmetic sequence.I can graph an arithmetic sequence function.An arithmetic sequence is a sequence of numbers in which the difference between each term is constant.There is a formula we can use to work with arithmetic sequences (explicit):.Qr =, +(n-1)-110nth term1st termTerm NumberDifference between termsSequence: 0, 4, 8, 12, ...A. Is this an arithmetic sequence? Why or why not? (2 points)B. If so, use the Explicit Formula above to create an equation to find the nth term. (13 points)C. Find the 18th term. (5 points)

Answer 1

A.

0, 4, 8, 12

This is an arithmetic sequence because the difference between terms is constant, as you can see:

`\begin{gathered} 4-0=4 \\ 8-4=4 \\ 12-8=4 \end{gathered}`

Therefore, the common difference is 4.

B.

Let:

`\begin{gathered} a_1=0 \\ a_n=a_1+(n-1)d \\ \text{where:} \\ d=4 \\ a_n=0+(n-1)d \\ a_n=(n-1)4 \end{gathered}`

C.

`\begin{gathered} n=18 \\ a_(18)=(18-1)4 \\ a_(18)=(17)4 \\ a_(18)=68 \end{gathered}`