SOLUTION: find a1 and the common ratio(r). given an=1, n=7, sn=1

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Question 934991: find a1 and the common ratio(r). given an=1, n=7, sn=1
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
find a%5B1%5D and the common ratio(r)if given a%5Bn%5D=1, n=7, s%5Bn%5D=1
we know that
a%5Bn%5D=a%5B1%5D%2B%28n-1%29d...plug in given values
1=a%5B1%5D%2B%287-1%29d
1=a%5B1%5D%2B6d...solve for d in terms of a%5B1%5D
d=%281-a%5B1%5D%29%2F6...........eq.1

we also know that the sum is:
s%5Bn%5D=%28n%2F2%29%28a%5B1%5D+%2Ba%5Bn%5D%29...plug in given values
1=%287%2F2%29%28a%5B1%5D+%2B1%29.........solve for a%5B1%5D
2=7%28a%5B1%5D+%2B1%29
2=7a%5B1%5D+%2B7
2-7=7a%5B1%5D+
-5=7a%5B1%5D+
highlight%28a%5B1%5D+=-5%2F7%29
go to d=%281-a%5B1%5D%29%2F6.....eq.1 plug in a%5B1%5D
d=%281-%28-5%2F7%29%29%2F6
d=%281%2B5%2F7%29%2F6
d=%2812%2F7%29%2F6
d=12%2F42....reduce, divide both numerator and denominator by 6
highlight%28d=2%2F7%29

check:
1=-5%2F7%2B%287-1%29%282%2F7%29
1=-5%2F7%2B%286%29%282%2F7%29
1=-5%2F7%2B12%2F7
1=7%2F7
1=1