# Thread: find the common ratio?

1. ## find the common ratio?

2.)The sum of a geometric series is -1023 and its first term is -3. If the last term is -768, what is the common ratio?

please supply you work if you have the time! i would like to understand this, as well as get a good grade!

2. Originally Posted by lollilikeslife
2.)The sum of a geometric series is -1023 and its first term is -3. If the last term is -768, what is the common ratio?

please supply you work if you have the time! i would like to understand this, as well as get a good grade!
You have a number of clues to help solve this..

Begin with the formula for the sum of a geometric series

$\displaystyle\ S_n=\frac{a\left(1-r^n\right)}{1-r}=\frac{a\left(r^n-1\right)}{r-1}$

Hence, you need three values.. $a,\;\;\;r,\;\;\;r^n$

You are given "a" and two clues to find the other two values.

$S_n=-1023$

$S_n=a+ar+ar^2+ar^3+......+ar^{n-1}$

hence you can find $r^{n-1}$ using the information given for the last term.

Also

$r^n=(r)r^{n-1}$

If you use these clues, you will get an equation in "r" which finds the value of "r".

3. ## Re: find the common ratio?

how to work the question

4. ## Re: find the common ratio?

Given a = -3
ar^{n} = -768
r^{n} = -768 / -3 = 256

so s = a (1 - r^{n}) / (1 - r)

change the sign on rhs

- 1023 = -3 (256 -1) / ( r -1)

r - 1 = -3(255)/ (-1023)

r = 1.7475 is the common ratio

If you need to know the value of n

1.7478....* n = 256
n log(10) (1.7478) = log (10) 256
n* 0.2425 = 2.4082
n = 9.93 approximately 10