Question

how would I find the nth term in the sequence 1 0 25 0 625.
I think the sin function has to be involved.

Answer 1

Do you need to write a function to solve this?

I would just notice what is given and you can infer the nth term.

Your sequence is based on f(n)=5^n, where n is an integer greater than or equal to 0.
n=0 --> 5^n = 5^0 = 1
n=1 --> 0
n=2 --> 5^n = 5^2 = 25
n=3 --> 0
n=4 --> 5^n = 5^4 = 625

When n is even, your sequence returns the value of the function. When n is odd, your function returns 0.

So if you wanted to find the nth term, whatever that term is, if you define n as an odd number, the value of the nth term is 0. If you define n as an even number, the value of the nth term is 5^n

Answer 2

why do odd numbers return to 0? Isn't 5^1 =5 and 5^3=125?

Answer 3

Yes, that's what I'm unsure of. I'm not sure if sitting on it longer would help me figure out a function for it specifically, but you are perfectly correct. For whatever reason, your function here returns 0 for all odd-numbered powers.

Answer 4

Maybe piece-wise actually....
Hang on that might work here!
Give me a sec.

Answer 5

I mean, I don't think this is needed, but I guess it technically would work here.