Question

What is the sum of an 8-term geometric sequence if the first term is 10 and the last term is
781,250?

Answer 1

\[2\times5^1 + 2\times5^2 + 2\times5^3+2\times5^4+2\times5^5+2\times5^6+2\times5^7+2\times5^8 = ?\]

Answer 2

976560

Answer 3

Could anyone please tell me how to find r? Because I have the formula, but I don't konw how to find r (the ratio)

Answer 4

I thought all you needed was the sum

Answer 5

Well, yes, that's all the problem asks for, but using the given formula, I can't solve it without knowing what r is. I have to show my work for the answer but I can't figure out how to find r.

Answer 6

What formula do you have?

Answer 7

Sn = a1 - anr/(1-r)
The an equals the last term and the r is, of course, the ratio.

Answer 8

r = last term/previous term = 2*5^2/2*5^1 = 5; r = 5

Answer 9

let's see if we get the same answer if we apply that

Answer 10

What did you get?

Answer 11

For some reason, I got 976550, instead of 976560, I'm off by like 10

Answer 12

\[\frac{(10-781250)5}{1-5}\]

Answer 13

Wait. r = last term?

Answer 14

r = 5, I posted that above :/

Answer 15

r is supposed to be the ratio between the terms in the sequence, not the last term. And yes, I saw that.

Answer 16

r = last term/previous term = 2*5^2/2*5^1 = 5; r = 5

Answer 17

I never said r was the last term

Answer 18

Ohhhh. Oh goodness, I'm sorry. I misread what you wrote. Seeing division problems written horizontally confuses me if I'm not paying strict attention.

Answer 19

What I posted was actually what happens when you put r into your formula:
\[\frac{(10-781250)5}{1-5} \]

Answer 20

Ohhhhhhh

Answer 21

But how did you get 5?

Answer 22

I know what happened

Answer 23

Would you mind joining me in a whiteboard room so you can show me what you're doing?

Answer 24

http://www.twiddla.com/594690 <-- that's the ling

Answer 25

Here's the formula:

\[\frac{10 - (781250*5)}{1-5}\]

Answer 26

*link

Answer 27

I have that same formula, but i still have the variable r in place of your 5s.
I don't understand how you came to that.

Answer 28

If you don't want to do the room thing, that's fine too. I hope you didn't think that was weird or creepy because that's definitely not how I intended it to seem.

Answer 29

I came to the room. You don't see my post?

Answer 30

r = 5, c'mon....Why are you not understanding this? In order to get the sum, you have to substitute everything, including r

Answer 31

Do you see my twiddla posts or not?

Answer 32

Yes!

Answer 33

Does it make any sense now?

Answer 34

How did you know what the binomial was?
That it was 2 x 5^1