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Periodic sequence with a period of 2 question.

I'm stuck on this sequence question where the sequence is periodic with a sequence of 2. For u2 I wrote it as 4+(4+(-1)^n) but I'm not sure how do calculate the sum because of the unknown n. (I'll post picture of question below)

Edit: Because I don't know n, I don't know if the - 1^n is - 1 or +1. How would I find that out?
(edited 4 years ago)
Question ii
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Original post by FutureMissMRCS
I'm stuck on this sequence question where the sequence is periodic with a sequence of 2. For u2 I wrote it as 4+(4+(-1)^n) but I'm not sure how do calculate the sum because of the unknown n. (I'll post picture of question below)

Edit: Because I don't know n, I don't know if the - 1^n is - 1 or +1. How would I find that out?

I'm not sure but you may be confusing this with recurrance relations? This is just a sum where you plug in the value of n:

u1=4+(1)1u_1 = 4 + (-1)^1

u2=4+(1)2u_2 = 4 + (-1)^2

u3=4+(1)3u_3 = 4 + (-1)^3

...

Try working out these and you'll notice a periodic sequence (use a calculator if you have to).
Original post by Notnek
I'm not sure but you may be confusing this with recurrance relations? This is just a sum where you plug in the value of n:

u1=4+(1)1u_1 = 4 + (-1)^1

u2=4+(1)2u_2 = 4 + (-1)^2

u3=4+(1)3u_3 = 4 + (-1)^3

...

Try working out these and you'll notice a periodic sequence (use a calculator if you have to).

Thank you,that works :smile: I think I overcomplicated the question in my head.

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