Calculus Examples

$1$ , $5$ , $25$ , $125$

Step 1

This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by $5$ gives the next term. In other words, $a_{n} = a_{1} r^{n - 1}$ .

Geometric Sequence: $r = 5$

Step 2

This is the form of a geometric sequence.

$a_{n} = a_{1} r^{n - 1}$

Step 3

Substitute in the values of $a_{1} = 1$ and $r = 5$ .

$a_{n} = 1 \cdot 5^{n - 1}$

Step 4

Multiply $5^{n - 1}$ by $1$ .

$a_{n} = 5^{n - 1}$