Algebra Examples

3

$3$ ,

- 6

$- 6$ ,

12

$12$ ,

- 24

$- 24$ ,

48

$48$ ,

- 96

$- 96$

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

- 2

$- 2$ gives the next term. In other words,

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

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

Geometric Sequence:

r = - 2

$r = - 2$

Step 2

This is the form of a geometric sequence.

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

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

Step 3

Substitute in the values of

a_{1} = 3

$a_{1} = 3$ and

r = - 2

$r = - 2$ .

a_{n} = 3 {(- 2)}^{n - 1}

$a_{n} = 3 {(- 2)}^{n - 1}$

Step 4

Substitute in the value of

n

$n$ to find the

n

$n$ th term.

a_{7} = 3 {(- 2)}^{(7) - 1}

$a_{7} = 3 {(- 2)}^{(7) - 1}$

Step 5

Subtract

1

$1$ from

7

$7$ .

a_{7} = 3 {(- 2)}^{6}

$a_{7} = 3 {(- 2)}^{6}$

Step 6

Raise

- 2

$- 2$ to the power of

6

$6$ .

a_{7} = 3 \cdot 64

$a_{7} = 3 \cdot 64$

Step 7

Multiply

3

$3$ by

64

$64$ .

a_{7} = 192

$a_{7} = 192$