Question

What is the 9th term of the geometric sequence where a1 = –5 and a6 = –5,120?

Answer 1

i cant seem to get the right answer, something is wrong in my steps

Answer 2

The equation for the 6th term is:
\[-5x ^{(6-1)}=-5120\]
\[5x ^{5}=5120\]
x = 4
Did you get this?

Answer 3

i have to use the formula an=a1r ^n-1
i can get all the way through the steps its just when i get where you have to take the square root its looks like this \[\sqrt[7]{1024?}\] i dont know how to do that

Answer 4

The 9th term is found as follows:
\[-5\times 4^{8}=-327680\]

Answer 5

how did you get -5 x 4^8 ?
like where did yiu get it from ?

Answer 6

Actually you needed to take the 5th root of 1024:
\[\sqrt[5]{1024}=(1024)^{1/5}=4\]
To calculate it I use the following function key on a calculator:
\[y ^{x}\]
entering 1024 for y and 1/5 for x

Answer 7

but why 5 and not 7 ?

Answer 8

Because the formula asks for (the position of the term - 1). So the calculation for the 6th term will have the power (6 - 1) = 5

Answer 9

it as for the 9th twerm

Answer 10

Good :)
The power in the calculation for the 9th term is (9 - 1) = 8

Answer 11

so i still dont get how to take the square root ? \[\sqrt[8]{1024?}\]

Answer 12

The common ratio r = 4
So using the formula you were given to find the 9th term you do the following:
(first term) * 4^(9 - 1) =\[-5\times 4^{(9-1)}=-5\times 4^{8}=-327680\]

Answer 13

i get that, where are you gettinh the 4 from?
since it didnt give you the common ratio

Answer 14

In the first posting i used x = common ratio. Your formula calls it r.
So x = r = 4 = common ratio

Answer 15

Do you mind working out thr problem ? cause im very confused.

Answer 16

I will get back to u in a few minutes :)

Answer 17

okat thank you

Answer 18

The formula looks like this.
\[a _{n}=a _{1}\times r ^{(n-1)}\]
a is a term in the series and n stands for the position. Suffix 1 after a identifies it as the first term. r is the common ratio
To find r (common ratio) substitute the value that is given for the 6th term into the formula as follows:
\[-5120=-5\times r ^{(6-1)}\]
\[5120=5\times r ^{(6-1)}=5\times r ^{5}\]
\[r ^{5}=5120\div5=1024\]
\[r=\sqrt[5]{1024}=4\]
Can you follow?

Answer 19

oh yes, i see you to the 6 from a6

Answer 20

\[a _{6}\]is the 6th term

Answer 21

yes then 6-1 is how you got 5, and yiu turn that into 1/5 ?

Answer 22

\[\sqrt[5]{1024}=1024^{(1/5)}\]

Answer 23

okay thank you