SOLUTION: 2) The third term of a G.P 12 and the first term is 48. Find the sum of the first 11 terms.

Algebra ->  Sequences-and-series -> SOLUTION: 2) The third term of a G.P 12 and the first term is 48. Find the sum of the first 11 terms.       Log On


   

Question 1128311: 2) The third term of a G.P 12 and the first term is 48. Find the sum of the first 11 terms.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
WE are given:
b%5B1%5D=48= the first term
b%5B3%5D=12= the third term

For a G.P. (geometric progression, geometric sequence in the USA),
with a common ratio r , the n%5Eth term is
b%5Bn%5D=b%5B1%5D%2Ar%5E%28n-1%29
The third term is given by that "formula" for n=3 as
b%5B3%5D=b%5B1%5D%2Ar%5E%283-1%29=b%5B1%5D%2Ar%5E2
Substituting into b%5B3%5D=b%5B1%5D%2Ar%5E2
48 for b%5B1%5D and 12 for b%5B3%5D we get
12=48%2Ar%5E2
12%2F48=r%5E2
1%2F4=r%5E2
Without more information, we cannot tell
if r=1%2F2=0.5 or r=-1%2F2=-0.5

For a G.P. the sum of the first n terms is given by
S%5Bn%5D=b%5B1%5D%28r%5En-1%29%2F%28r-1%29

For n=11 we get
S%5B11%5D=48%28r%5E11-1%29%2F%28r-1%29

IF r=0.5 :
S%5B11%5D=48%280.5%5E11-1%29%2F%280.5-1%29
S%5B11%5D=48%280.000244140625-1%29%2F%28-0.5%29
S%5B11%5D=48%28-0.999755859375%29%2F%28-0.5%29
S%5B11%5D=48%2A0.4998779296875
S%5B11%5D=95.953125

IF r=-0.5 :
S%5B11%5D=48%28%28-0.5%29%5E11-1%29%2F%28-0.5-1%29
......
S%5B11%5D=48%280.000244140625-1%29%2F%28-1.5%29
...............
S%5B11%5D=32.015625