Question

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

an = 3 • (-4)^n + 1

an = 3 • 4^n - 1

an = 3 • (-4)^n - 1

an = 3 • 4^n

Answer 1

\(\LARGE\color{black}{ a_5=a_2 \times r^{3-1} }\)

Answer 2

first find the common ratio.

Answer 3

whats r??

Answer 4

786=-12*r^3-1

Answer 5

I think I was wrong

Answer 6

so 786/-12=r^2

Answer 7

oh ok

Answer 8

\(\Large\color{black}{ a_5=a_2 \times r^{5-2} }\)

\(\Large\color{black}{ a_5=a_2 \times r^{3} }\)

\(\Large\color{black}{ 786=(-12) \times r^{3} }\)

Answer 9

(this is also logical, because otherwise you get an imaginary ratio)

Answer 10

ok so 768/-12=r^3
-64=r^3

Answer 11

-4=r

Answer 12

yes,

Answer 13

So the first term \(\Large\color{black}{ a_1 }\) is equal to ?
(Knowing that the 2nd term is `-12` , and ` r=-4 ` )

Answer 14

3

Answer 15

Yes.

Answer 16

Yes.

Answer 17

so what do i do from there?

Answer 18

The recursive formula (for the nth term) is like this,

\(\Large\color{black}{ a_n=a_1 \times r^{(n-1)} }\)

all you have to do is to `fill in your numbers`

Answer 19

you found that \(\Large\color{blue}{ a_1=3 ~~~~~\rm{and}~~~~~r=-4}\)

Answer 20

so its the third answer?

Answer 21

yes, assuming that it is

an = 3 • (-4)^\(\normalsize\color{red}{ (}\)n-1\(\normalsize\color{red}{ )}\)

see what I am adding? It's important.

Answer 22

ok thank you :)

Answer 23

Anytime! This was one of my favorite topics in school.
Take care:)