Question

Find the least value for n for which Sn is greater than 163.
a1 = 4, r = .98

Answer 1

Answer: The answer is n=84

Answer 2

n = 84

Explanation:

The sum is given by the formula ...

Sn = a1·(1 -r^n)/(1 -r)

We can fill in the given values and solve for n.

163 = 4(1 -0.98^n)/(1 -0.98)

163·0.02/4 = 1 -0.98^n

0.98^n = 1 -0.815

n·log(0.98) = log(0.185)

n = log(0.185)/log(0.98) ≈ 83.52

A value of n=84 will give a sum greater than 163.

_____

S84 ≈ 163.3545

S83 ≈ 162.6067