Question

What is the sum of the geometric sequence 2, 10, 50, … if there are 8 terms?

Answer 1

`195312`

Explanation:

Since the sequence is geometric, there is a constant ratio given by `r=x_(n+1)/x_n=10/2=50/10=5`

The first term is `a=2`.

The formula for the sum to n terms of such a geometric series is given by :

`sum_(k=1)^n ar^(k-1)=(a(1-r^n))/(1-r)`

So in this particular case it becomes

`sum_(n=1)^8 2*(5)^(n-1)=(2(1-5^8))/(1-5)=195312`.