Question

Pre calculus help!
Find the sum of the first six terms of the geometric sequence for which a2=0.7 and a3=0.49

Answer 1

Do you have the formula for the sum of a geometric sequence?

Answer 2

I know the equation you use is Sn=a1(1-r^n)/1-r

Answer 3

Yep, good. Se we need to identify a1, r, and n. Any ideas on a1?

Answer 4

I also know that we have to find the difference between 0.7 and 0.49

Answer 5

which will get us to what r is equal to

Answer 6

but I am hvai

Answer 7

Well, r is the common ratio since this is a geometric sequence.

Answer 8

having trouble with those calculations because I dont know if its 1/7 or 0.7

Answer 9

The common ratio can be found using \[\frac{ a _{n+1} }{ a _{n} }\]

Answer 10

so 0.49+1/0.7

Answer 11

No, the +1 is in the subscript. Meaning take the ratio of a term divided by the term before it.

Answer 12

In this case, .49/.7

Answer 13

Oh I see, when I calculate that I get 1/7

Answer 14

or .7

Answer 15

1/7 isn't .7

Answer 16

7/10 is .7

Answer 17

oh then .7

Answer 18

Right, good. So that is r.

Answer 19

What do you think a1 is?

Answer 20

I think we use a2 which is 0.7 and then divide that by the common ration r=.7
When I did that I got 1 because .7/.7 =1

Answer 21

Yep, perfect. :-)

Answer 22

And how about n?

Answer 23

Okay and then the equation for the sum is S6=1(1-.7^6)/

Answer 24

.7

Answer 25

n=6 because thats the numbers we have in the sum

Answer 26

well no, the numbers we are using to find the sum

Answer 27

Right, good. But in my equation, the denominator is 1-.7

Answer 28

Okay yeah thats how I plugged it in and I came up with S6=.182351

Answer 29

Hm, that's not what I get.