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Evaluate the indicated term for each arithmetic sequence.$$2,4,6, \ldots ; \quad a_{24}$$
48
Precalculus
Chapter 14
Sequences and Series
Section 2
Arithmetic Sequences
Introduction to Sequences and Series
Introduction to Combinatorics and Probability
Johns Hopkins University
Harvey Mudd College
University of Michigan - Ann Arbor
Boston College
Lectures
07:16
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01:37
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01:31
we're being asked to find a cell 24. Meaning we want to find the 24th term the sequence. So to do this, we're going to use our A seven formula. So we have a seven is equal to a sub one, plus the quantity of and minus one times D. Well, we need to know what ace of one is. Well, remember, Ace of one is the first term in the sequence, which in this case, is too. Next we need our own value, which in this case, represents which term the sequence working for Well, we're looking for a sub 24 which means we're trying to find the 24th term. So N is 24 and lastly, we need d remember D represents our common difference is what we're adding to get from one term to the next. Well, to get from to the four we're gonna add to so d is equal to two. So now in order the fine days of 24 we're going to substitute all these values into our formula. So we're gonna have a set of 24 is equal to a someone which is to plus N, which is 24 minus one times D would just to and now we just need to evaluate. Well, 24 minus one is 23 23 times two is 46. So we have a set of 24 is equal to two plus 46 2 plus 46 is 48. So what we found is that the 24th term in the sequence is 48.
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