Question 984035
a sub n=a1 * r^n-1
a6=10
a16=0.1

Let a6 be the first term of the modified sequence.
0.1=10*r^10
10^-2=r^10=0.01
r= 0.01^(1/10)=0.6309.  Without rounding.
a1=100
a11=1

Sum=a1 (1-r^n)/1-r
=100*(.9)/1-r
=90/(1-r); 1-r=0.3691(rounded)
unrounded, answer is 243.87.

If one keeps the same ratio, which isn't quite 0.6, this works out exactly.  If one rounds to 0.6, it does not.