Question

What is the 6th term of the geometric sequence where a1 = 1,024 and a4 = -16?
I'm not sure how to find the r without knowing the second term

Answer 1

( 1024 + (-16) )/4, u get 260

Answer 2

i mean -260 which is ur r

Answer 3

ur 6th term would then be -16-260-260 which will be -536

Answer 4

so then would i take -16 and minus 260 from it 2 more times?

Answer 5

yes

Answer 6

hint:

a2 = a1*r

a2 = 1024r

------------

a3 = a2*r

a3 = 1024r*r

a3 = 1024r^2


------------

a4 = a3*r

a4 = 1024r^2*r

a4 = 1024r^3

-16 = 1024r^3

now solve for r

Answer 7

uhm, that actually is not one of the answers x3 @ 11 calc
Select one:
a. 1
b. -0.25
c. -1
d. 0.25

and @ jim, I'm not understanding.

Answer 8

basically each term is found by multiplying the previous term by the common ratio r

Answer 9

the second term a2 is found by multiplying the previous term a1 by r

that's why a2 = a1*r

Answer 10

and why a3 = a2*r

Answer 11

Yeah, I understand that. But the only thing i could think to do is to divide the a1 by 2, but I can tell that's not what i need to do

Answer 12

a1 does NOT mean "a times 1"

a2 does NOT mean "a times 2"

etc

so you can't pull out that 2 and divide by it

Answer 13

do you see how I got -16 = 1024r^3 ?

Answer 14

uhm yes i think i understand, so a2 would be 1024r? so a16 would be 1024r^15?

Answer 15

exactly

Answer 16

so because a4 = 1024r^3, and a4 = -16, we know that


a4 = 1024r^3

-16 = 1024r^3

-16/1024 = r^3

-1/64 = r^3

r^3 = -1/64

r = cube root of (-1/64)

r = -1/4


once you know this value of r, you can use it to find any term you want

Answer 17

Okay, thank you! I got -1, is that correct?

Answer 18

let me check

Answer 19

Oh i already answered it and it was right ^-^ thank you for your help

Answer 20

yes -1 is correct, and I'm glad it agrees, you're welcome