Algebra Examples

$1$ , $4$ , $16$ ; dots

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 $4$ gives the next term. In other words, $a_{n} = a_{1} r^{n - 1}$ .

Geometric Sequence: $r = 4$

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 $r = 4$ .

$a_{n} = 1 \cdot 4^{n - 1}$

Step 4

Multiply $4^{n - 1}$ by $1$ .

$a_{n} = 4^{n - 1}$