\(a_n = a_1 r^{n-1}\)
\(a_6 = a_1 r^{6-1}\)
\(4 = a_1 r^5\)
\(a_40 = a_1 r^{10-1}\)
\(a_10 = a_1 r^{10-1}\)
\(\frac{4}{81} = a_1 r^9\)
Divide the two equations to eliminate \(a_1\)
\(\frac{4}{81(4)} = \frac{a_1r^9}{a_1r^5}\)
\(\frac{1}{81} = r^4\)
\(r=\frac{1}{3}\) Answer