A geometric series has third term and sixth term a) find the first and the common ratio of the series.I am able to solve this one which...

Hello!

I agree with your answer to the part a), the only possible series is  

The question b) becomes simple if we recall the formula of the sum of terms of a geometric progression with the common ratio

I give the more general form of the common formula because sometimes there is a confusion related with the starting index...

Hello!

I agree with your answer to the part a), the only possible series is  

The question b) becomes simple if we recall the formula of the sum of terms of a geometric progression with the common ratio

I give the more general form of the common formula because sometimes there is a confusion related with the starting index of the sum (0 or 1). In this from, the sum is

((the last summed up term of the series) - (the first summed up term of the series)) above (the common ratio - 1).

We know already that    and

Therefore    and the sum is equal to

Hence the statement we need to prove is true and  K = 2. This is the answer.