SOLUTION: The sum of a geometric series is 57232. The common ratio is 2 and the last term is 28672. What is the first term?

Question 36552: The sum of a geometric series is 57232. The common ratio is 2 and the last term is 28672. What is the first term?
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
The sum of a geometric series is 57232. The common ratio is 2 and the last term is 28672. What is the first term?
FORMULA FOR N TH TERM IS ....
TN=A*R^(N-1)..HENCE
28672=A*2^(N-1).......................I
FORMULA FOR SUM IS
SN=A*{R^N - 1 }/(R-1)...HENCE
57232 = A*(2^N-1)/(2-1)=A*(2^N-1)....................II
EQN.II/EQN.I...
57232/28672=A*(2^N -1)/{A*2^(N-1)}=(2^N -1)/2^(N-1)
57232/28672=2^N/2^(N-1) - 1/2^(N-1)=2-1/2^(N-1)
1/2^(N-1)=2-57232/28672=(57344-57232)/28672=112/28672
2^(N-1)=28672/112=256=2^7
N-1=7�.OR��N=8�SUBSTITUTING IN EQN.I�
28672=A*2^(8-1)=256A�..OR�..A = 28672/256=112
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