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Explain when you would use each of the two formulas for $S_{n}$.
Precalculus
Chapter 14
Sequences and Series
Section 2
Arithmetic Sequences
Introduction to Sequences and Series
Introduction to Combinatorics and Probability
Johns Hopkins University
Campbell University
Harvey Mudd College
Utica College
Lectures
07:16
In mathematics, a continuo…
04:09
00:36
Write down the two formula…
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In the formula for $S_{n},…
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00:57
Solve each formula for the…
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01:07
00:42
01:14
The point $P$ lies in the …
Solve the formula for a.
01:36
and this problem. We're being asked to determine when we should use each of the two, uh, some formulas. So I wrote down our choose summation formulas. So let's take a look at the first formula versus the second. So the first formula says S seven is equal to end over two times the quantity of a plus one plus a seven versus our second formula is s a pen equals and over two times the quantity of two times a sub one claws the quantity of and minus one times t. So notice what they have familiar in each formula. They both have end. You need end to use each formula, and you both need a serve one. And I realized there was an end. Here is well, so what's the difference? Well, to use the first formula, you need to have a say event, so this formula needs a seven. If you don't have a seven, you can't use it versus the second formula. Notice it's other term is D. So in this case, if you don't have a seven, but you have de, then you can use the second formula. And so that's really the main difference between the two. So if you have the IMF term in the sequence, you can use the first one. If you know your common difference and don't know the end term, you can use the second formula. But no matter what, you always have tohave and an ace of one in order to use either of these formulas.
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