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Question 74007:
Found 2 solutions by jim_thompson5910, psbhowmick:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The ratio r is the factor to get from term to term. So
r=nth term/(n-1) term
r=8%2F4=2
r=2
The sequence doubles each term, so the sequence is 2%5En
So the 24th term is
2%5E23=8388608(n=23 zero is the 1st term)
The sum of a geometric series is
S=a%281-r%5En%29%2F%281-r%29where a=1
S=%281-2%5E10%29%2F%281-2%29
S=%281-1024%29%2F%28-1%29
S=1023
So the sum of the first ten terms is 1,023

Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!
a) Common ratio = 2%2F1+=+4%2F2+=+8%2F4+=+2

b) The n-th term is given by t%5Bn%5D+=+ar%5E%28n-1%29 where a is the first term and r is the common ratio.
Here n = 24, a = 1, r = 2.
So, t%5B24%5D+=+1%2A2%5E%2824-1%29+=+2%5E23%29

c) The sum of the first n-terms is given by S%5Bn%5D+=+a%28r%5En-1%29%2F%28r-1%29.
Here n = 10, a = 1, r = 2.
So S%5B10%5D+=+1%282%5E10-1%29%2F%282-1%29+=+%282%5E10-1%29%2F1+=+2%5E10-1+=+1024+-+1+=+1023