the sum of 4 + 12 + 36+ 108+ ... +tn is 4372. How many terms are in the series?
2 years ago
At the Math 11 level, there will be problems involving two types of series. This series is a geometric one because each term is 3 times the one before.There is a formula for the sum of a geometric series. This formula will usually be given to you on a formula sheet.Sn=t1[(rn-1)/(r-1)] , (assuming r is not equal to 1)
t1 is the first term of the series. For this one, it is 4.
r is the common ratio. That is 3 for this one. Each term is 3 times the previous one.
sn is 4372, that is the sum of the first n terms.
From here, we use algebra to solve the equation for rn (= 3n).
4372 = 4[(3n-1)/(3-1)]
2187=3n Now we need a way to find what power of 3 = 2187.
If you haven't learned to use logarithms yet, then maybe trial and error would be quicker.
Keep multiplying 3s until you reach 2187.
It will take 7 of them. 3x3x3x3x3x3x3=2187 so n=7.
I hope this has helped you.