Open Question: Maths Question about Arithmetic-Geometric Progressions…?
Given that:
Arithmetic Progression:
U1=a ,
U2=a+d ,
U3=a+2d ,
U4=a+3d ,
…
Un=a+(n-1)d
and Un=[ Un-1 + Un+1 ] / 2
Geometric Progression:
U1=a ,
U2=ar ,
U3=ar^2 ,
U4=ar^3 ,
…
Un=ar^(n-1)
and Un=sqrt[ Un-1 x Un+1 ]
Arithmetic-Geometric Progression:
U1=a ,
U2=(a+d)r ,
U3=(a+2d)r^2 ,
U4=(a+3d)r^3 ,
…
Un=[ a+(n-1)d ] r^(n-1)
and Un=[ r Un-1 + Un+1 / r ] / 2
My question is is there a formula for obtaining Un (for an AGP) by just using Un-1 and Un+1 without having to find r , or is it impossible ?
Thanks.
Source:Open Question: Maths Question about Arithmetic-Geometric Progressions…?
