Problem

Evaluate the number of terms in each arithmetic s…

01:51

Problem 23 Hard Difficulty

Evaluate the number of terms in each arithmetic sequence.
$$
3,5,7, \ldots, 33
$$

Answer

16

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Precalculus

Beginning and Intermediate Algebra

Chapter 14

Sequences and Series

Section 2

Arithmetic Sequences

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Video Transcript

we're being asked how many terms are in the given sequence. 357 all the way. The 33. Well, because we're being asked how many terms air in the sequence that means we're looking for. Okay, well, what else do we know? Well, we know ace of one. That's the first term in the sequence in this case is three. We know the IMF terminus sequence. That's the last term. So a sub n is equal to 33 and we can also find our common difference, which is d remember, common differences, what we add to get for one turn to the next, which in this case, we just keep adding to which means our common differences, too. So now we're going to use to formula to find the M for turning the sequence to solve. For n remember, our formula is a seven is equal to a serve one plus the quantity of and minus one times D. So now we'll substitute the values that we just found into this formula. So a seven we said was 33 equals ace of one, which is three plus we don't know. End. That's what we're looking for and then times D, which is to. So now we just have to solve this equation. So the first thing I'm gonna do is subtract three from both sides and 33 Ministry is 30. So this is equal two and minus one times two. So now what I can do next is divide both sides by two. Well 30 divided by two is 15. So we have 15 is equal to end minus one. So the salt for end we add one to both sides and 15 plus one is 60. So what that means is that there are 16 terms in this sequence.

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