Question Number 10487 by Saham last updated on 13/Feb/17

A sequence of numbers T_1 ,T_2 ,T_3 ,....... T_(n ) satisfies  the relation T_(n + 1)  + n^2  = nT_n  + 2 for all integers  n≥1. if T_1  = 2. find   (a) The values of T_2 , T_3 , T_4   (b) An expression for T_n  in terms of the sequence  (c) The sum of the first nth terms of the sequence  (d) The sum of T_n  + T_(n + 1)  + T_(n + 2)   when n = 20

Answered by mrW1 last updated on 17/Feb/17

 T_(n + 1)   = nT_n  + 2−n^2   (a)  T_1 =2  T_2 =1×T_1 +2−1^2 =2+2−1=3  T_3 =2×T_2 +2−2^2 =6+2−4=4  T_4 =3×T_3 +2−3^2 =12+2−9=5  (b)  T_n =n+1  (c)  S(n)=Σ_(k=1) ^n T_k =2+3+4+...+(n+1)=((n(n+1))/2)  (d)  T_(20) +T_(21) +T_(22) =21+22+23=66

Commented bySaham last updated on 18/Feb/17

I really appreciate sir.