Find the 5th Term 3 , -12 , 48 , -192

$3$ , $- 12$ , $48$ , $- 192$

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 $a_{1} = 3$ and $r = - 4$ .

$a_{n} = 3 {(- 4)}^{n - 1}$

Step 4

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

$a_{5} = 3 {(- 4)}^{(5) - 1}$

Step 5

Subtract $1$ from $5$ .

$a_{5} = 3 {(- 4)}^{4}$

Step 6

Raise $- 4$ to the power of $4$ .

$a_{5} = 3 \cdot 256$

Step 7

Multiply $3$ by $256$ .

$a_{5} = 768$

Find the 5th Term 3 , -12 , 48 , -192

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