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Geometric series help?
How would you find Sn for a geometric series if a1 or r is not given?
a2= - 36, a5=972, n=7
I tried using the equation an=a1 x r^n-1 but that would work...so how would I start this problem if someone could help? You don't need to give me the answer just what I would have to do to start it.
1 Answer
- Violet WLv 71 decade agoFavorite Answer
How about this?
a2 and a5 are 3 factors apart, meaning n increased by 3.
So let's find the cube root of the ratio to find out what the multiplier must have been.
(927/-36)^(1/3) = (-27)^(1/3)
You can't take the cube root of a negative number, but if the multiplier is negative, then the terms alternate in sign as follows:
a2 -
a3 +
a4 -
a5 +
That works, so find the cube root of 27 and then apply the negative:
-(27)^)(1/3) = -3
The multipler should be -3.
Then a1 = a2/(-3) = -36/(-3) = 12
Prototype formula:
an = 12 x (-3)^(n-1)
Check:
a1 = 12 x (-3)^0 = 12
a2 = 12 x (-3)^1 = 36
a5 = 12 x (-3)^4 = 12x(81) = 972
The above check.
Calculate the answer:
a7 = 12 x (-3)^6 = 12x(729) = 8748 <==ANSWER
