Question

Find the value of the 10th term in the sequence of partial sums of 5(2/3)^n.

Answer 1

1: 5
2: 5+ 5(2/3)
3: 5+ 5(2/3) + 5(2/3)^2 = 5(1 + 2/3 + (2/3)^2)
4: 5(1 + 2/3 + (2/3)^2 + (2/3)^3)

What else?

Answer 2

I understand the concept, but I'm trying to compute it using the formula a(1-r^n)/(1-r) but am not sure which values go where :$

Answer 3

Right. What's preventing you from doing that?

3: 5+ 5(2/3) + 5(2/3)^2 = 5(1 + 2/3 + (2/3)^2) = \(5\cdot\dfrac{1 - (2/3)^3}{1-(2/3)}\)
4: 5(1 + 2/3 + (2/3)^2 + (2/3)^3) = \(5\cdot\dfrac{1 - (2/3)^4}{1-(2/3)}\)