Find the 5th Term 2 , -8 , 32 , -128

$2$ , $- 8$ , $32$ , $- 128$

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 $a_{1} = 2$ and $r = - 4$ .

$a_{n} = 2 {(- 4)}^{n - 1}$

Step 4

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

$a_{5} = 2 {(- 4)}^{(5) - 1}$

Step 5

Subtract $1$ from $5$ .

$a_{5} = 2 {(- 4)}^{4}$

Step 6

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

$a_{5} = 2 \cdot 256$

Step 7

Multiply $2$ by $256$ .

$a_{5} = 512$

Find the 5th Term 2 , -8 , 32 , -128

Related Questions

Support LCMGCF.com by disabling your adblocker.