Find the 8th Term 4 , -24 , 144 , -864 , 5184 , -31104

$4$ , $- 24$ , $144$ , $- 864$ , $5184$ , $- 31104$

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 $- 6$ gives the next term. In other words, $a_{n} = a_{1} r^{n - 1}$ .

Geometric Sequence: $r = - 6$

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 $r = - 6$ .

$a_{n} = 4 {(- 6)}^{n - 1}$

Step 4

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

$a_{8} = 4 {(- 6)}^{(8) - 1}$

Step 5

Subtract $1$ from $8$ .

$a_{8} = 4 {(- 6)}^{7}$

Step 6

Raise $- 6$ to the power of $7$ .

$a_{8} = 4 \cdot - 279936$

Step 7

Multiply $4$ by $- 279936$ .

$a_{8} = - 1119744$

Find the 8th Term 4 , -24 , 144 , -864 , 5184 , -31104

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