Geometric Progression – Sequences and Series | Mathematics | Page 1

raven stump Jul 9, 2025, 3:15 PM

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Can anyone teach me how to solve? I think it's involve log

undone jayBOT Jul 9, 2025, 3:15 PM

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raven stump Can anyone teach me how to solve? I think it's involve log

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nocturne owl Jul 9, 2025, 3:23 PM

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raven stump Can anyone teach me how to solve? I think it's involve log

I assume you're trying to solve for q and n?
If so, note that you can take the logarithm (base doesn't matter, so let's say ln) of both equations, which will then become linear in n and ln(q).

raven stump Jul 9, 2025, 3:26 PM

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I see wait i try

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nocturne owl Jul 9, 2025, 3:42 PM

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Well, now apply the same logarithm property to the last line as the one you did for the first equation.

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Then you get a system in n and ln(q).

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Probably better to look at this generally, though. Then the system would be:
q*x^(n - 1) = T
q(1 - x^n)/(1 - x) = S
You can solve this for q and n, then substitute your values of x, T and S.

raven stump Jul 9, 2025, 4:06 PM

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I think I got it

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Is it correct?

nocturne owl Jul 9, 2025, 4:07 PM

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raven stump Is it correct?

Yeah. Though, I do recommend solving this generally, too.

raven stump Jul 9, 2025, 4:09 PM

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Hm but I'm not sure how to solve it generally tho..

nocturne owl Jul 9, 2025, 4:11 PM

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We have:
q*x^(n - 1) = T
q(1 - x^n)/(1 - x) = S
Try expressing q from the first equation and substituting into the second.

raven stump Jul 9, 2025, 4:16 PM

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nocturne owl Jul 9, 2025, 4:20 PM

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Right.
We need n, so you can multiply both parts by (1 - x)/T. Then you can simplify the left side.

raven stump Jul 9, 2025, 4:25 PM

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nocturne owl Jul 9, 2025, 4:28 PM

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Well, now you can factor out x^n, then take the logarithm.

raven stump Jul 9, 2025, 4:47 PM

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nocturne owl Jul 9, 2025, 4:49 PM

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Yeah, looks good.

raven stump Jul 9, 2025, 4:54 PM

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nocturne owl Jul 9, 2025, 4:55 PM

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Nice!
Also, you can solve for q generally, too, by substituting n into q = Tx^(1 - n). The expression becomes quite simple.

raven stump Jul 9, 2025, 4:56 PM

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Ah i see, I'll look into it too. Anyway thank you so much, I appreciate it🙏

nocturne owl Jul 9, 2025, 5:01 PM

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You're welcome!

river reef Jul 9, 2025, 6:52 PM

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Balls

raw yewBOT Jul 10, 2025, 7:00 PM

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@raven stump

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raven stump Jul 10, 2025, 7:00 PM

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+close

raw yewBOT Jul 10, 2025, 7:00 PM

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raven stump +close

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raw yewBOT Jul 10, 2025, 7:01 PM

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raw yew

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#Geometric Progression – Sequences and Series