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.

$a_1=12\\\\a_2=\dfrac{1}{2}a_1+1=\dfrac{12}{2}+1=6+1=7 \\ \\a_3=\dfrac{1}{2}a_2+1=\dfrac{7}{2}+1=\dfrac{9}{2}$

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