Algebra Examples

$- 8$ , $- 24$ , $- 72$ , $- 216$ , $- 648$ , $- 1944$ , $- 5832$ , $- 17496$

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 $a_{1} = - 8$ and $r = 3$ .

$a_{n} = - 8 \cdot 3^{n - 1}$

Step 4

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

$a_{10} = - 8 \cdot 3^{(10) - 1}$

Step 5

Subtract $1$ from $10$ .

$a_{10} = - 8 \cdot 3^{9}$

Step 6

Raise $3$ to the power of $9$ .

$a_{10} = - 8 \cdot 19683$

Step 7

Multiply $- 8$ by $19683$ .

$a_{10} = - 157464$