This is a new topic for GCSE but I'm finding that it's not being taught well / at all in schools.
Firstly, if you don't already know, a geometric progression/sequence is a sequence where to get from one term to the next you need to multiply by a number. This is different to an arithmetic sequence where you add to get from one term to the next.
E.g. 2, 4, 8, 16, 32,...
This is a geometric sequence where the ratio between terms (the multiplier) is equal to 2.
This sequence has nth term
2nIn general, a sequence with first term
a and ratio
r has nth term
arn−1.
To show that a sequence is geometric, you just need to show that there is a constant ratio between terms.
So for part a), first write out the sequence and then explain that the ratio is constant. E.g. the first term will be 1000.
Have a go at that and post your ideas if you get stuck.
If you're familiar with compound interest, then you'll find that part b) can be done in a very similar way.