SOLUTION: find the number of terms of a geometric sequence with, first term 1/64, common ratio 2 and the last term 512 please i need help please help.....

Question 195831: find the number of terms of a geometric sequence with, first term 1/64, common ratio 2 and the last term 512
please i need help please help.....
Answer by RAY100(1637) (Show Source): You can put this solution on YOUR website!
std form is a(n) = a(1) r^(n-1)
.
a(1)=1/64,,,,given
.
r = 2,,,,given
.
a(n) = 512,,,,given
.
substituting
.
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
.
check
.
a(16) = (1/64) *2^ (16-1) =(1/64) * 2^15 = 512 ok
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