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Fill the series 5,7,17,47,115,? find the value in the "?".

 Feb 2, 2016

Best Answer 

 #4
avatar+26397 
+40

Fill the series 5,7,17,47,115,? find the value in the "?".

 

The function is:

an=(n10)d0+(n11)d1+(n12)d2+(n13)d3+(n14)d4an=d0+(n1)d1+12(n1)(n2)d2+1312(n1)(n2)(n3)d3+141312(n1)(n2)(n3)(n4)d4an=d0+(n1){d1+(n2)[12d2+(n3)(16d3+124(n4)d4)]}an=d0d1+d2d3+d4+n(12d118d2+22d325d412)+n2(12d224d3+35d424)+n3(4d310d424)+n4(d424)

 

we have:

 

d0=5d1=2d2=8d3=12d4=6

 

an=d0d1+d2d3+d4+n(12d118d2+22d325d412)+n2(12d224d3+35d424)+n3(4d310d424)+n4(d424)an=52+812+6+n(122188+221225612)+n2(1282412+35624)+n3(41210624)+n4(624)an=512n+34n212n3+14n4an=512n+34n212n3+14n4

 

laugh

 Feb 2, 2016
edited by heureka  Feb 2, 2016
edited by heureka  Feb 2, 2016
edited by heureka  Feb 2, 2016
edited by heureka  Feb 2, 2016
edited by heureka  Feb 2, 2016
edited by heureka  Feb 2, 2016
edited by heureka  Feb 2, 2016
 #1
avatar+33658 
+15

One possibility is 245:

 

sequence

.

 Feb 2, 2016
 #2
avatar+118703 
0

Very impressive but how did you work it out Alan?  

 

It wasn't even in the oeis ....

 Feb 2, 2016
 #3
avatar+26397 
+5

Fill the series 5, 7, 17, 47, 115, ?  find the value in the "?".

 

d0=5717471151. Difference d1=21030682. Difference d2=820383. Difference d3=12184. Difference d4=6

 

 an=(n10)d0+(n11)d1+(n12)d2+(n13)d3+(n14)d4 

 

an=(n10)5+(n11)2+(n12)8+(n13)12+(n14)6a6=(50)5+(51)2+(52)8+(53)12+(54)6a6=15+52+108+1012+56a6=5+10+80+120+30a6=245

 

laugh

 Feb 2, 2016
 #4
avatar+26397 
+40
Best Answer

Fill the series 5,7,17,47,115,? find the value in the "?".

 

The function is:

an=(n10)d0+(n11)d1+(n12)d2+(n13)d3+(n14)d4an=d0+(n1)d1+12(n1)(n2)d2+1312(n1)(n2)(n3)d3+141312(n1)(n2)(n3)(n4)d4an=d0+(n1){d1+(n2)[12d2+(n3)(16d3+124(n4)d4)]}an=d0d1+d2d3+d4+n(12d118d2+22d325d412)+n2(12d224d3+35d424)+n3(4d310d424)+n4(d424)

 

we have:

 

d0=5d1=2d2=8d3=12d4=6

 

an=d0d1+d2d3+d4+n(12d118d2+22d325d412)+n2(12d224d3+35d424)+n3(4d310d424)+n4(d424)an=52+812+6+n(122188+221225612)+n2(1282412+35624)+n3(41210624)+n4(624)an=512n+34n212n3+14n4an=512n+34n212n3+14n4

 

laugh

heureka Feb 2, 2016
edited by heureka  Feb 2, 2016
edited by heureka  Feb 2, 2016
edited by heureka  Feb 2, 2016
edited by heureka  Feb 2, 2016
edited by heureka  Feb 2, 2016
edited by heureka  Feb 2, 2016
edited by heureka  Feb 2, 2016
 #5
avatar+33658 
0

I just fitted a 4th order polynomial to the sequence.  f(n)=Σ4k=0aknk

 

There are five unknowns (the ak) and five numbers in the sequence.

 Feb 2, 2016
 #6
avatar
+5

5            7               17             47               115                 X  (245)

      +2            +10           +30             +68               +130

 

 

             +8               +20             +38           +62

 

 

                     +12               +18              +24

 

                               +6                 +6

 

 

 

18+6=24

38+24=62

68+62=130

115+130=245

 Feb 27, 2016

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