Question

Find an expression for the \(n\)th term of the sequence.  \(10,50,250,1250, \ldots\)

Answer 1

\[
\begin{array}{ll}
10,50,250,1250, \ldots & a_{1}=10=2(5)=2\left(5^{1}\right) \\
& a_{2}=50=2(25)=2\left(5^{2}\right) \\
& a_{3}=250=2(125)=2\left(5^{3}\right) \\
& a_{4}=1250=2(625)=2\left(5^{4}\right)
\end{array}
\]
Based on this pattern, \(a_{n}=2\left(5^{n}\right)\).