Question

The sum of a geometric series containing five terms, a common ratio of 3, and a first term of 1/2 is 62.5.

Answer 1

The general form of a geometric series is the following:

`u_n=u_1r^n` wherein u_n is the first term and r the ratio.
So,

`u_n= (1)/(2) 3^n`
The sum of N first terms is given by the formula:

`S_N=u_1 (1-r^N)/(1-r)\\= (1)/(2) (1-3^N)/(1-3)\\= -(1)/(4)(1-3^N)`
The number of terms is 5, so we get the formula:

`-(1)/(4)(1-3^5)=62.5\\ -(1)/(4)(1-243)=62.5\\ -(1)/(4)(-242)=62.5\\ 60,5=62.5`
The sum is rather 60.5 than 62.5