SOLUTION: the second term of the geometric series is 2 and 12th term is 1/256 then the first term is? A)4 B)2 C)1 D)8

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Question 919168: the second term of the geometric series is 2 and 12th term is 1/256 then the first term is?
A)4
B)2
C)1
D)8
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
given:
the second term of the geometric series is 2 and 12th term is 1%2F256 then the first term is
Form: a%28n%29+=+ar%5E%28n-1%29
----------------------
a%2812%29+=+ar%5E11+=+1%2F256
a%282%29+=+ar+=+2
Divide a(12) by a(2) to solve for "r":
ar%5E11%2Far=%281%2F256%29%2F2

cross%28a%29r%5Ecross%2811%29%5E10%2Fcross%28a%29cross%28r%29=%281%2F256%29%2F2

r%5E10+=+1%2F512

r%5E10+=+0.001953125

r+=+root%2810%2C0.001953125%29

r+=+0.5263157894736842 or proximately

r+=+0.5 or r=1%2F2

go to ar+=+2, plug in r=1%2F2 and solve for a

a%281%2F2%29=+2
a=+2%2A2
a=+4

answer: A)4