Question 195831
std  form  is  a(n) = a(1) r^(n-1)
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a(1)=1/64,,,,given
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r = 2,,,,given
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a(n) = 512,,,,given
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substituting
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512 = (1/64) * 2^  (n-1)
32768 = 2^(n-1)
log  both  sides
log 32768 = log 2^(n-1) = (n-1) log2
log 32768 / log 2 = n-1
15 = n-1
n=16,,,,  ANSWER
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check
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a(16) = (1/64) *2^ (16-1) =(1/64) * 2^15 = 512  ok