if the following sum represents a geometric series, then what is its value?

Question

5 + 15 + 45 + ... + 98,415

Answer 1

Hi Peter,

 

The ratio of the series is 15/5= 3, so r=3

We need to find the number of terms. n, in the series first.

n^th term is equal to

a_n = a_1*r^(n-1)

98415 = 5*3^(n-1)

n-1 = 9

n = 10

 

Sum of the first 10 terms is equal to

S₁₀ = a₁*[(1-r^n)/(1-r)]

= 5*[(1-3^10)/(1-3)]

= 147620