Find the 8th Term -3 , -12 , -48 , -192 , -768 , -3072

$- 3$ , $- 12$ , $- 48$ , $- 192$ , $- 768$ , $- 3072$

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 $r = 4$ .

$a_{n} = - 3 \cdot 4^{n - 1}$

Step 4

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

$a_{8} = - 3 \cdot 4^{(8) - 1}$

Step 5

Subtract $1$ from $8$ .

$a_{8} = - 3 \cdot 4^{7}$

Step 6

Raise $4$ to the power of $7$ .

$a_{8} = - 3 \cdot 16384$

Step 7

Multiply $- 3$ by $16384$ .

$a_{8} = - 49152$

Find the 8th Term -3 , -12 , -48 , -192 , -768 , -3072

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