\( a_{n+1}=5 ^n a_n\)

Calculus Level 1

The sequence \(\{a_n\}\) satisfies \(a_1=1\) and \[ a_{n+1}=5 ^n a_n \text{ for } n \geq 1.\]

For what value of \(k\) do we have \(a_k=5 ^{276}\)?

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