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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.