Question

Im learning about Recursive and Explicit in Pre-Calc, and it says to use the rule to write the first three terms of each sequence. I have no idea how to figure these out. Only know the first one or two because they give it to you but I have no idea how to figure out for a third one. Someone PLZ HELP!!!!!!!

Answer 1

Hello,

4. you have sequences defined by the first term and a recursive relation.

`a_1=3\\\\a_n=2a_(n-1) \ \ \text{ for n}> 1`

Take n = 2, it gives

`a_2=2a_1` , right?

But you know
`a_1=3`

so
`a_2=2a_1=2*3=6`

This is the second term. You are asked to find the first three terms.

Now, let's take n = 3

`a_3=2a_2=2*6=12`

So the first three terms are 3, 6, 12.

6.

`a_1=12\\\\a_2=(1)/(2)a_1+1=(12)/(2)+1=6+1=7 \\ \\a_3=(1)/(2)a_2+1=(7)/(2)+1=(9)/(2)`

8.

`a_1=10\\ \\a_2=-3a_1=-3*10=-30\\\\a_3=-3a_2=-3*(-30)=90`

10.

`a_1=2\\\\a_2=-1\\\\a_3=a_2+a_1=-1+2=1\\\\a_4=a_3+a_2=1-1=0`

Do not hesitate if you have any question.

Thank you