Algebra Examples

$1$ , $3$ , $9$ , $27$ , $81$ , $243$

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 $3$ gives the next term. In other words, $a_{n} = a_{1} r^{n - 1}$ .

Geometric Sequence: $r = 3$

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 $r = 3$ .

$a_{n} = 1 \cdot 3^{n - 1}$

Step 4

Multiply $3^{n - 1}$ by $1$ .

$a_{n} = 3^{n - 1}$

Step 5

Substitute in the value of $n$ to find the $n$ th term.

$a_{7} = 3^{(7) - 1}$

Step 6

Subtract $1$ from $7$ .

$a_{7} = 3^{6}$

Step 7

Raise $3$ to the power of $6$ .

$a_{7} = 729$