Formula for the first n pairs of

algebra precalculus - Formula for number of pairs that can be made from $n$ items - Mathematics Stack Exchange

Imagine the sequence of whole numbers from 1 to 10 written out. What is the general formula for geometric series? Sal is illustrating this principle in a general form, showing how it applies to ANY arithmetic sequence. Try it in your head with a simple series, such as whole numbers from 1 to 10, to see what I mean.

Sorry about this question but, what is the difference between a arithmetic sequence and a arithmetic series. Want to join the conversation? William Kitchen. The fundamental insight that originally led to the creation of this formula probably started with the observation that the sum of the first term and last term in an arithmetic series is always the same as the sum of the 2nd and 2nd-to-last, 3rd and 3rd-to-last, etc.

Beth C. Posted 10 years ago. Then imagine the same sequence written in reverse order just below the first. No need to write all that out every time. Next, we'll see that this formula is equivalent to multiplying the average of the first and last terms by the number of terms. Bella Estelle Olegario. Learn how to write an arithmetic sequence in general terms, using a common difference d and a first term a.

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5 ways to represent a relation

Kyle Krol. Log in. Arithmetic series. This is because as you move from one pair to the next, the upper term increases by the same amount that the lower term decreases. Griffen Eastwood. It also leaves no confusion about what to do with the middle term when there are an odd number of terms. Posted 9 years ago. Σ It has lower limit a as 1, upper limit as 4, then,Σ, a a Just for example: What if we have sigma notation?

Writing a sequence forward then backward, one above the other, is just another way to look at that same phenomenon because it aligns the first term with the last term, 2nd term with 2nd-to-last, etc.

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I can't seem to wrap my brain around this topic. Ali Zain. The purpose of all that is to illustrate why the formula works. Flag Button opens signup modal. I understand that it works in finding the series, but I don't understand why it works. At Downvote Button opens signup modal. If there is one.

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Show preview Show formatting options Post answer. Why does Sal swap the order of the sequence and add it to itself?

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