geometric series help!

So, you have everything that you need

Also, if the sum of the first four terms is 5468.75 and the first term is 2000.Find the common ratio if all the terms are positive

Also, if the sum of the first four terms is 5468.75 and the first term is 2000.Find the common ratio if all the terms are positive

You have to be able to do this yourself

You know the rule for the sum of n terms

You know a

This is an easy question

The problem is that for those students whose default reaction to every question they can not start is to ask a friend the internet has been in many cases a retrograde development lol .

This is what I've got but the answer is 3/4

You can't cancel like that! The r has to be in all the terms so... And where did your 1 disappear to?

Sn = a(1-r^n)/(1-r)

Put your numbers in. Then post back with what you have.

5468.75=2000-2000(-r^4)/1-r

So you have

5468.75 = (2000 - 2000r^4)/(1-r)

You want to get rid of the bottom so multiply by tha y

Is what I have correct?

I do not intend to worry you but some of your basic algebra skill (photo of work) are awful - you need to practice some GCSE level skills

What you have done now is correct but there are some short cuts

From $5468.75 = \dfrac{2000(1-r^4)}{1-r}$ it would have made sense to recognise that the numerator is the difference of 2 squares (twice) then a cancelling can happen

You will still have a cubic and that cubic would be more easily found just by writing the first 4 terms down and putting the total = 5468.75