Submitted 20 hours ago by LGTM@discuss.tchncs.de to [deleted]
https://discuss.tchncs.de/pictrs/image/dd357048-5812-406b-9205-12c7265b98dc.png
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
For someone who sucks at math, would you be able to give a TL;DR on what a geometric sequence is?
Each value in a geometric sequence is found by multiplying the previous value by a constant. e.g. 1,2,4,8,16,32,… with r = 2 and N1 = 1
A geometric sequence is a sequence (that is an ordered list of numbers, usually following some pattern). The nth number in this sequence (a_n) can be generated by multiplying the base a by r^n, so a_2 would be a*r^2. Hope that makes it clear!
I can mostly get it. I would probably have to see examples in practice to fully grasp it.
To clarify, this is not A * 2 but rather the 2nd Term of A, hope that helps clarify any potential confusion.
FishFace@piefed.social 19 hours ago
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.
Bazell@lemmy.zip 9 hours ago
I suppose that this specification was said to make the task look more complicated to solve. Just a simple obstacle.