Question

What is the 6th term of the geometric sequence where a_1 = −4,096 and a_4 = 64?

Answer 1

@agent0smith @ikram002p

Answer 2

\[\large a_n = a_1 r^{n-1}\]You're given \[a_1=-4096\], and you know \[a_4=64\]use a4 to find r.

Answer 3

\[\large a_4 = a_1 r^{4-1}=64\]

Answer 4

you mean 64=-4096^4-1 @agent0smith

Answer 5

Yes

Answer 6

i still didnt get the answer im doing something wrong i dont know what

Answer 7

First find r.\[\Large -4096 r^{3}=64\]
Then find term 6 \[\Large a_6 = -4096 r^{6-1} =\]

Answer 8

isnt it 4-1 first?

Answer 9

And 4-1 is equal to...

Answer 10

oh ok then 64/-4096=-0.015625 then square it 3sqrt-0.015625

Answer 11

I don't know what this means " then square it 3sqrt-0.015625"

You have \[\Large r^3 = -0.015625\]find r by taking the cube root.

Answer 12

0.375

Answer 13

right?

Answer 14

No... use a calculator, or wolfram alpha. Put that number to the power of 1/3.

Answer 15

ugh why 1/3 its 3 no?

Answer 16

\[\Large r^3 = -0.015625\]Putting both sides to the power of 1/3 gives \[\Large r= \sqrt[3]{−0.015625}\]

Answer 17

Or \[\Large r= (−0.015625)^{1/3}\]

Answer 18

-0.25?

Answer 19

pls reply @agent0smith

Answer 20

Yes

Answer 21

No, its -4.