What is the sum of the first 15 terms of the geometric series: 1/6 1/2 3/2 9/2 ... 7174453 4782968.6667 797161.4444 1195742.1667
?
1 answer:
Sum of geometric sequence
for the sum where the initial value is a₁ and the common ratio is r and the term is n
![S_n= \frac{a_1(1-r^n)}{1-r}](https://tex.z-dn.net/?f=S_n%3D%20%5Cfrac%7Ba_1%281-r%5En%29%7D%7B1-r%7D%20)
1/6, 3/6, 9/6
hmm
times 3 every time
common ratio is 3
a₁=1/6
n=15
![S_15= \frac{(1/6)(1-3^15)}{1-3}](https://tex.z-dn.net/?f=S_15%3D%20%5Cfrac%7B%281%2F6%29%281-3%5E15%29%7D%7B1-3%7D%20)
![S_15= \frac{(1/6)(1-14348907)}{-2}](https://tex.z-dn.net/?f=S_15%3D%20%5Cfrac%7B%281%2F6%29%281-14348907%29%7D%7B-2%7D%20)
![S_15= \frac{(1/6)(-14348906)}{-2}](https://tex.z-dn.net/?f=S_15%3D%20%5Cfrac%7B%281%2F6%29%28-14348906%29%7D%7B-2%7D%20)
![S_15= \frac{-2391484.33333333}{-2}](https://tex.z-dn.net/?f=S_15%3D%20%5Cfrac%7B-2391484.33333333%7D%7B-2%7D%20)
![S_15= 1195742.16666666](https://tex.z-dn.net/?f=S_15%3D%201195742.16666666%20)
answer is 1195742.16666666 or your last answer
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