Expert: Richard J. Raridon - 7/11/2006

Question
What is Sn of the geometric series with a1=4, an=256, and n=4?
A)84
B)260
C)336
D)340

I did this two different ways:
Using this formula-
Sn= [n(a1+an0]/2
I got 520

Then I did it using a 4 term series:
4,__, __, 256
4-256=252
252/3=84
84+4=88
88+84=172
4+88+172+256=520

So, I got 520 both times, but thats not one of my choices. Did I do this correctly?


Answer
No, you don't understand geometric series.  
If the first term is 4 then the next terms are
4r, 4r^2, 4r^3, 4r^4, etc., where r is the ratio between terms, and is the same between any pairs of terms.  So you have 4r^3 = 256.  Now see if you can find the middle terms.