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A sequence satisfied #T_n=(T_(n-1)-T_(n+1))/2#, with #T_1=3# and #T_2=7#, find #T_4#.

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Answer 1 · 2018-05-11T13:30:34

29

It would help to rewrite the recurrence relation in the form

#T_{n+1}=T_{n-1}-2T_n#

So, putting #n=2#, we get

#T_3 = T_1-2T_2 = 3-2times 7 = 3 -14 = -11#

and for #n=3#

#T_4 = T_2-2T_3 = 7-2times (-11) = 29#