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Worked example: sequence explicit formula

Video transcript
If a sub n is equal to n squared minus 10 over n plus 1, determine a sub 4 plus a sub 9. Well let's just think about each of these independently. a sub 4-- let me write it this way. a the fourth term, so a sub 4-- so our n, our lowercase n, is going to be 4-- is going to be equal to-- where everywhere we see an n in this explicit definition for this sequence, everywhere we see an n, we would replace it with a 4. So it's going to be equal to 4 squared minus 10 over 4 plus 1, which is equal to-- well let's see-- that's 16 minus 10 over 5, which is equal to 6 over 5. So that is a sub 4. That is the fourth term. Now let's think about a sub 9. So a sub 9. So once again, everywhere that we see an n, we would replace it with a 9. We're looking at when lowercase n is equal to 9, or we're looking at the ninth term. So it's going to be 9 squared-- in that blue color just so we see what we're doing-- 9 squared-- do it in the green color-- minus 10 over 9 plus 1 is equal to-- well, in the numerator, we have 81 minus 10 over 10, over 9 plus 1. And so this is going to be equal to 71 over 10. Now they want us to sum these two things, so that's going to be equal to 6/5. a sub 4 is 6/5 plus a sub 9, which is 71 over 10. Well, we can rewrite 6/5 as being equal to 12/10 and then 71/10, so plus 71 over 10, which is equal to-- well, if I have 12/10 and then I have another 71/10, then I'm going to have 83/10. And we're done.