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
Hence, you need three values..
You are given "a" and two clues to find the other two values.
hence you can find using the information given for the last term.
Also
If you use these clues, you will get an equation in "r" which finds the value of "r".
Here is the Solution Hope this will help you,
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