Question

Geometric Sequence help anyone?

List the next four terms of a geometric sequence with t1 = 4 and tn = -3tn-1.

A. 12, 36, 108, 324
B. 12, 36, 48, 60
C. -12, 36, -108, 324
D. -12, 36, -48, 60

*If you'd rather walk me through the steps versus giving me the answer I'd appreciate that also!

Answer 1

"tn = -3tn-1" is really written

\[\Large t_{n} = -3t_{n-1}\]

I'm assuming

Answer 2

I'm still confused on how I go about solving this problem

Answer 3

If that assumption is correct, it means that the nth term \(\Large t_{n}\) is found by multiplying the previous term \(\Large t_{n-1}\) by -3

Answer 4

t1 is the first term

t1 = 4

so the first term is 4

Answer 5

t2 is the second term

you find t2 by multiplying the first term (t1) by -3 because of that rule that defines the nth term

Answer 6

so what is t2?

Answer 7

In other words,

\[\Large t_{2} = -3*t_{1}\]

what is \(\Large t_{2}\) ?

Answer 8

what is the value of t alone again? 4?

Answer 9

t has no value

but when we say t1, t2, t3, etc etc...we're talking about the first term, second term, third term, etc etc...

Answer 10

initially, we are given

\[\Large t_{1} = 4\]

this is the first term

Answer 11

How do I find the second term? I'm sorry, it's been a long day my brain is working slow

Answer 12

you multiply -3 by the previous term to get the next term

Answer 13

that's exactly what this rule means

\[\Large t_{n} = -3t_{n-1}\]

Answer 14

\(\Large t_{n}\) is the nth term

\(\Large t_{n-1}\) is the term just before the nth term (the previous term of the nth term)

Answer 15

Oh okay, that makes more sense!

Answer 16

I think I got it from here, thank you so much for your help!

Answer 17

you're welcome