Solving this recursion question

Question

Text-only

For the sequence $10,50,250,1250,\ldots$

1. Determine the first form $a$ and the common ratio $r$.
2. Infer an explicit formula for this sequence.
3. Write its recursive form.

Please check, if answer is correct? If wrong, please show correct step to do?

Answer 1

Your answers under (1) and (3) are correct .

To answer second question :

Explicit formula for this sequence is :

$a_n=2\cdot 5^n$ with $n\ge 1$

Answer 2

Your work is correct. Note that your recurrence relation needs an initial condition. In this case,

$$ U_1 = 10.$$