Question

Please Help!!

Find an equation for the nth term of a geometric sequence where the second and fifth terms are -21 and 567, respectively.

Answer 1

@SolomonZelman @precal @paki @jdoe0001

Answer 2

well you need to use your formulas for geometric sequences to figure out your common ratio

Answer 3

\(\large\color{blue}{ a_2 \times r^{5-2}=a_5 }\)

Answer 4

-12*r^3=567

Answer 5

-21*

Answer 6

r^3=588

Answer 7

to get from the 2nd term
to the 5th term
you'd need to multiply the currrent term TIMES some number, namely the "common ratio" or "r"

so as SolomonZelman said, it went from the 2nd to 5th, that 3 terms furhther up
meaning "r" was used 3 times, so \(\bf r^3\)

Answer 8

576/-21

Answer 9

\(\large\color{blue}{ a_2 \times r^{5-2}=a_5 }\)

\(\large\color{blue}{ (-12) \times r^{3}=567 }\)

\(\large\color{blue}{ r^{3}=567 \div (-12)}\)

\(\large\color{blue}{ r^{3}=-47.25}\)

Answer 10

Oh it is 21, not 12. Sorry.... but you get the idea.

Answer 11

-27=r^3
7=r

Answer 12

\(\large\color{blue}{ -27= (-3)^3}\)

Answer 13

\(\large\color{blue}{ 27= 3^3}\)

Answer 14

hmm \(\Large \bf -21r^3=567\implies r=\sqrt[3]{-\cfrac{\cancel{ 567 }}{\cancel{ 21 }}}\)

Answer 15

so its a_n=7*3^n-1

Answer 16

Yes

Answer 17

yeap

Answer 18

thanks!!

Answer 19

yw

Answer 20

`\(\large\color{black}{ a_n = 7 \times 3 ^ {n -1 } }\) `
Copy and paste the text:)
@ninjasandtigers

Answer 21

Is it Solomon Zelalem

Answer 22

No, close:) Zelman

Answer 23

Have a good luck !