Find the 8th Term 7/9 , -7/3 , 7 , -21 , 63 , -189 , 567 ,

$\frac{7}{9}$ , $- \frac{7}{3}$ , $7$ , $- 21$ , $63$ , $- 189$ , $567$ ,

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 $- 3$ gives the next term. In other words, $a_{n} = a_{1} r^{n - 1}$ .

Geometric Sequence: $r = - 3$

Step 2

This is the form of a geometric sequence.

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

Step 3

Substitute in the values of $a_{1} = \frac{7}{9}$ and $r = - 3$ .

$a_{n} = \frac{7}{9} {(- 3)}^{n - 1}$

Step 4

Combine $\frac{7}{9}$ and ${(- 3)}^{n - 1}$ .

$a_{n} = \frac{7 {(- 3)}^{n - 1}}{9}$

Step 5

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

$a_{8} = \frac{7 {(- 3)}^{(8) - 1}}{9}$

Step 6

Simplify the numerator.

Subtract $1$ from $8$ .

$a_{8} = \frac{7 {(- 3)}^{7}}{9}$

Raise $- 3$ to the power of $7$ .

$a_{8} = \frac{7 \cdot - 2187}{9}$

Step 7

Simplify the expression.

Multiply $7$ by $- 2187$ .

$a_{8} = \frac{- 15309}{9}$

Divide $- 15309$ by $9$ .

$a_{8} = - 1701$

Find the 8th Term 7/9 , -7/3 , 7 , -21 , 63 , -189 , 567 ,

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