Question

Terms of aSequence Use a graphing calculator to do the following. (a) Find the first ten terms of the sequence.

(b) Graph the first ten terms of the sequence.

$a_n=a_{n-1}-a_{n-2}and{a}_1=1,a_2=3$

Short answer

1. The first 10 terms of the sequence are:$1,3,2,-1,-3,-2,1,3,2,-1$.

b. The graph is:

Step-by-step solution

a.Step 1.  Given

The given sequence is$a_n=a_{n-1}-a_{n-2}and{a}_1=1,a_2=3$.

Step 2.  To determine

Find the first ten terms of the sequence.

Step 3.  Calculation

We will use Desmos graphing calculator.

We enter the given expression $a_n=a_{n-1}-a_{n-2}and{a}_1=1,a_2=3$.Then enter values for n.$n=1,2,3,\mathrm{.....},10$respectively.

So, the first 10 terms of the sequence are:$1,3,2,-1,-3,-2,1,3,2,-1$

b.Step 1.  Given

The given sequence is$a_n=a_{n-1}-a_{n-2}and{a}_1=1,a_2=3$.

Step 2.  To determine

Graph the first ten terms of the sequence.

Step 3.  Calculation

From part (a), the first 10 terms of the sequence are:

$1,3,2,-1,-3,-2,1,3,2,-1$

Then we plot them: