Find the 5th Term -4 , -16 , -64 , -256

$- 4$ , $- 16$ , $- 64$ , $- 256$

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

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

Step 4

Multiply $- 4 \cdot 4^{n - 1}$ .

Factor out negative.

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

Raise $4$ to the power of $1$ .

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Subtract $1$ from $1$ .

$a_{n} = - 4^{n + 0}$

Add $n$ and $0$ .

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

Step 5

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

$a_{5} = - 4^{5}$

Step 6

Raise $4$ to the power of $5$ .

$a_{5} = - 1 \cdot 1024$

Step 7

Multiply $- 1$ by $1024$ .

$a_{5} = - 1024$

Find the 5th Term -4 , -16 , -64 , -256

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