1.2 General Term of an Arithmetic Sequence (part I)

[TDotShaunaDot]

thank you so much!

[omgitswes32]

what about a sequences that's (5, 1, 5, 1, 5, 1, ....)

what would the d be? + or - 4? it's kind of confusing

[donalduncan]

@omgitswes32 Good question. (5, 1, 5, 1, 5, 1, ...) is a sequence, but it is not an "arithmetic" sequence. An arithmetic sequence has the same difference between every pair of terms, and in your example, as you rightly said, the difference changes between +4 and -4. So we can't use the formula for the general term of an arithmetic sequence.

If you wanted to find the general term of this sequence, you could just say that tn = 5 if n = odd number, and tn = 1 if n = even number.

[omgitswes32]

@donalduncan okay thanks, I also found another answer as. T(n) = 2(-1)^n + 3.

That's more along the lines of what I was looking for but still have no idea how that answer was came upon. I understand what you did with when n = odd, tn = 5 and so on. Seems like some of these are just guess and check, which is very frustrating.

[donalduncan]

@omgitswes32 The best answer I can give for "how to come up with that" is this... Think about (5, 1, 5, 1...) as being 3 + 2 for odd # terms, and 3 - 2 for even # terms. The way to alternate the +/- would be the (-1)^n, because if n is odd, it will be -1, and if n is even, it will be +1. Multiply that factor by 2, so that it becomes -2 or +2... Then your equation becomes T(n) = -2(-1)^n + 3. It needs to be -2 so that you can get 5 for the first term, instead of 1... tough one!

[omgitswes32]

@donalduncan ah! thank you, all it required was a bit extra thinking. Thanks a lto

[chrisv20]

Thank you for posting this video.