The given geometric sequence is [tex] a_n = 2 * 5^{n-1} [/tex]
The general formula for geometric sequence is [tex] a_n = a* r^{n-1} [/tex]
From this two equations
a = 2 and r = 5
Where 'a' is the first terms and 'r' is the common ratio
In geometric sequence each term is obtained by multiplying the previous term by common ratio. In recursive formula , we multiply the previous term by common ratio.
We know common ratio is 5. so we multiply previous term by 5 to get recursive formula.
The recursive formula for the given geometric sequence,
[tex] a_n = a_{n-1} * 5 [/tex]
