If b is the first term of an infinite G.P. whose sum is five, then b lies in the interval.

first term=b
common ratio=r
|r|<1
for infinte series
For infinite series ;S=b/(1-r)=5
→b=5(1-r)
Since |r|<1 for an infinite geometric series to converge, we have
-1<r<1
→0<1-r<2
→0<b<10.
So option (0,10) is the correct answer.
interval of b∈(0,10)