Question

Which of the following recursive formula represent the same geometric sequence as an=2•5^(n-1)?

Answer 1

The given geometric sequence is $a_n = 2 * 5^{n-1}$

The general formula for geometric sequence is $a_n = a* r^{n-1}$

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,

$a_n = a_{n-1} * 5$