Post #127701
2026-01-12 22:36 UTC
The nth term of a geometric sequence can be written
a(n) = a(1)*r^(n-1)
We can rewrite the two given equations:
a(2) + a(4) = 30 = a(1)*r + a(1)*r^3 (Equation 1)
a(3) + a(5) = 15 = a(1)*r^2 + a(1)*r^4 (Equation 2)
Notice that Equation 1 can be substituted into Equation, i.e.,
a(1)*r^2 + a(1)*r^4 = 15
r*[a(1)*r + a(1)*r^3] = 15
r*(30) = 15
r = 1/2
If we substitute this into Equation 1, we have
a(1)/2 + a(1)/8 = 30
a(1) = 30 * 8/5 = 48
The answer is 48.
Sauce: The Last Adventurer, Ch. 103
Replies (3)
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@FishFace@piefed.social 2026-01-12 23:40
Yeah, it makes no sense to specify that the sum exists; the finite sum always exists, and even if you were talking about the infinite sum, it makes no odds on what the first term is.
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@FiniteBanjo@feddit.online 2026-01-12 22:56
To clarify, this is not A * 2 but rather the 2nd Term of A, hope that helps clarify any potential confusion.
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@Bubs@lemmy.zip 2026-01-13 07:17
For someone who sucks at math, would you be able to give a TL;DR on what a geometric sequence is?