Question

Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are -12 and 768, respectively.

Answer 1

i understand how to do this when the two terms are already consecutive, but im not sure where to start with this one

Answer 2

what is the ratio?

Answer 3

how do i find the ratio without two consecutive terms?

Answer 4

Grr...

Answer 5

:x
sorrry

Answer 6

im not just looking for an answer, i legitimately want help understanding how to work the problem, i just need help through most of it

Answer 7

Yeah..i'm trying to work it out to explain it to you,but having difficulty finding the ratio.

Answer 8

Would knowing the ratio r be helpful?

Answer 9

a2 = -12

a3 = a2*r = -12r

a4 = a3*r = (-12r)*r = -12r^2

a5 = a4*r = (-12r^2)*r = -12r^3

Answer 10

because a5 = 768, we can say

768 = -12r^3

Answer 11

There you go, now you can solve for r

Answer 12

nice!

Answer 13

so,
768/-12 = r^3
-64 = r^3
-4 = r

Answer 14

an = a1(-4)^n-1

Answer 15

im sorry, but now now how would i find the first term to use in the rule?

Answer 16

show me how you have the form above? an?
one more question, does your prof ask you have to prove what you claim before using it to find our the nth term?

Answer 17

*out

Answer 18

a subscript n

Answer 19

Use the idea

Second term = (First term)*r

Answer 20

nth term = (first term)(ratio)^n-1

Answer 21

that was the basis of my lesson. im virtual schooled, so the lessons are very impersonal, leaving much to the student to figure out on their own

Answer 22

\[\large a_{2} =?\]\[\large r=?\]\[\large a_{1}=?\] plug into equation \[\large a_{2}=a_{1}*r\]

Answer 23

or a1 = a2/r

Answer 24

would it be
an = 3(-4)^n-1

Answer 25

yep

Answer 26

okay, thank you all