The sequence S₁, S₂,S₃ ,...... is defined by:

S₁ = 211, S₂ = 375, S₃= 420, S₄ = 523, and:
S_n= S_n-1- S_n-2+ S_n-3- S_n-4

Find S₅₃₁+ S₇₅₃+ S₉₇₅

S1=A
S2=B
S3=C
S4=D
S5=D-C+B-A
S6=(D-C+B-A)-D+C-B=-A=-S1
S7=-A-(D-C+B-A)+D-C=-B=-S2
S8=-B-(-A)+(D-C+B-A)-D=-C=-S3
S9=-C-(-B)+(-A)-(D-C+B-A)=-D=-S4
S10=-D-(-C)+(-B)-(-A)=-D+C-B+A=-S5

So S(n)=S(n+10) and S(n)=-S(n+5)

S₅₃₁+ S₇₅₃+ S₉₇₅=S₁+ S₃+ S₅ = D+B = 523+375 = 898

Posted by Jer on 2015-10-29 16:31:34