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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 a 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 over 4 plus 1 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 9th term so it's going to be 9 squared let me do that blue color just so we see what we're doing 9 squared in the green color minus 10 over 9 plus 1 over 9 plus 1 is equal to well in the numerator we have 81 minus 10 81 minus 10 over 10 over 9 plus 1 and so this is going to be equal to 70 1 over 10 now they want us to sum these two things so that's going to be equal to it's going to be equal to 6/5 a sub 4 6 fifths plus a sub 9 which is 71 over 1070 1 over 10 but we can rewrite 6 fifths as being equal to 12 tenths 12 tenths and then 71 tenths so plus 71 over 10 which is equal to well if I have 12 10th and then I have another 70 110 so now I'm going to have 83 10 eighty-three tents and we're done