Question 933241
53,477,4293,38637,347733

Take to the 4th differences to get them all the same

Assume a 4th degree polynomial 
{{{a[n]=An^4+Bn^3+Cn^2+Dn+E}}}
Substitute n=1,2,3,4,5 and solve the resulting 5x5 system
of equations:

{{{a[n]=expr(27136/3)x^4-expr(257792/3)x^3+expr(291148/3)x^2-expr(407182/3)x+192973}}}

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2,5,10,17,26,

Easy. That's 1 more than the sequence of squares 1,4,9,16.25

{{{a[n]=n^2+1}}}

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 -2,-8,-18,-32,-50

Easy.  That's -2 times the sequence of squares 1,4,9,16.25

{{{a[n]=-2n^2}}}

Edwin</pre>