Concept:
We need to identify the relation between \(50\) and \(65\), and apply the same relation to \(290\).
Step 1: Express \(50\) and \(65\).
\[
50=49+1=7^2+1
\]
\[
65=64+1=8^2+1
\]
So the relation is:
\[
7^2+1 \rightarrow 8^2+1
\]
Step 2: Express \(290\).
\[
290=289+1=17^2+1
\]
So the corresponding next number should be
\[
18^2+1
\]
Step 3: Calculate.
\[
18^2+1=324+1
\]
\[
=325
\]
Step 4: Final answer.
\[
\boxed{325}
\]
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