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TMUA Maths help - geometric and arithmetic series

Started going through TMUA past papers and just struggling with this question, I'd really appreciate if someone could explain it to me. Thanks - answer is D.
https://imgur.com/a/M1aKixY
Reply 1
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RichE
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Original post by jackwhurt
Started going through TMUA past papers and just struggling with this question, I'd really appreciate if someone could explain it to me. Thanks - answer is D.
https://imgur.com/a/M1aKixY

What are expressions for the first, second and fourth terms?
What does it mean for those three terms to be consecutive terms of an arithmetic progression?
What is the sum-to-infinity formula?
Reply 2
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jackwhurt
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Original post by RichE
What are expressions for the first, second and fourth terms?
What does it mean for those three terms to be consecutive terms of an arithmetic progression?
What is the sum-to-infinity formula?

1. 4, 4+n, 4+2n
2. Change by same amount each time
3. (had to look this up, haven't seen it before) S∞ = a / 1-r

So a would = 4 but not sure what to do next
Reply 3
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RichE
15
Original post by jackwhurt
1. 4, 4+n, 4+2n
2. Change by same amount each time
3. (had to look this up, haven't seen it before) S∞ = a / 1-r

So a would = 4 but not sure what to do next

I was expecting an answer to 1 in terms of a and r. The answer to 1 is more what I was expecting for an answer to 2.
you can rule out A and B as they are both less than 4.
Reply 5
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jackwhurt
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Original post by RichE
I was expecting an answer to 1 in terms of a and r. The answer to 1 is more what I was expecting for an answer to 2.

a, ar, ar^3?
Reply 6
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jackwhurt
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Original post by jackwhurt
a, ar, ar^3?

So now I can form equations
Original post by jackwhurt
1. 4, 4 n, 4 2n
2. Change by same amount each time
3. (had to look this up, haven't seen it before) S∞ = a / 1-r

So a would = 4 but not sure what to do next


- How can you write the first, second and fourth terms of the geometric progression in terms of r and the first term?

- Knowing that these are the first three consecutive terms in an arithmetic progression, can you make any equations using the terms to find r? What happens between consecutive terms in an arithmetic progression?

I know I’m basically repeating what RichE said but I hope I’m adding a few more hints.
(edited 4 years ago)
Reply 8
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jackwhurt
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Original post by GrayestOwl0900
- How can you write the first, second and fourth terms of the geometric progression in terms of r and the first term?

- Knowing that these are the first three consecutive terms in an arithmetic progression, can you make any equations using the terms to find r? What happens between consecutive terms in an arithmetic progression?

I know I’m basically repeating what RichE said but I hope I’m adding a few more hints.

Thanks mate, got it
Reply 9
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jackwhurt
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Original post by RichE
I was expecting an answer to 1 in terms of a and r. The answer to 1 is more what I was expecting for an answer to 2.

Thanks mate, got it
Reply 10
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jackwhurt
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Original post by BuryMathsTutor
I don't know whether there are other solutions available but mine are here, in case they help.

http://burymathstutor.co.uk/TMUA_specimen_solutions.pdf

Thanks man helps a lot
328E44DA-7CA7-4D9D-A0A4-80059412C1BE.jpg.jpeg

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