Question

What is the 6th term of the geometric sequence where a1 = 625 and a3 = 25?

Answer 1

Gotta do it manually.
\(\text{1st term} : 5^{4} \qquad 2nd:5^3 \cdots 4th:5^1\cdots 6th:{5^{-1}}\)

Answer 2

So, what's \(5^{-1}\)?

Answer 3

1/5 ?

Answer 4

Jshak, do you know how to define a geometric seq?

Answer 5

That's correct! You may answer amistre's question.

Answer 6

a list of numbers that share a common ratio?

Answer 7

correct :)

Answer 8

That's very correct!

Answer 9

Do you know the common ratio here? :)

Answer 10

um 1/5?

Answer 11

Aha!

Answer 12

so the answer is 0.2 !

Answer 13

thank you both!! (:

Answer 14

You're welcome!
And I didn't help you, it was just you who did the work :)

Answer 15

Also, 0.2 is another correct notation for 1/5 ;)

Answer 16

(:

Answer 17

a1 = a1
a2 = a1*r
a3 = a1*r*r = a1*r^2
a4 = a1*r*r*r = a1*r^3

following this pattern we can contiue

a5 = a1*r^(5-1)
a6 = a1*r^(6-1)

an = a1*r^(n-1)

we know a1 and a3

a3: 625*r^2 = 25

r^2 = 25/625

r = sqrt(25/625)

r = 5/25 = 1/5
-----------------------------

to find a6

a6 = a1*r^5
= 625*(1/5)^5 = .2, yes :)