Given the recursive formula below, which of the following equations is a correct explicit formula for the sequence?

$$ a_1=10 $$ $$ a_{n+1} = 2a_n $$

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The recursive formula implies that each successive term is double the previous. This is a geometric sequence with starting term 10 and ratio 2.

$$ a_n=a_1\cdot r^{n-1} $$ $$ \boxed{a_n=10 \cdot 2^{n-1}} $$