Find the 6th Term 2 , -14 , 98 , -686

$2$ , $- 14$ , $98$ , $- 686$

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 $- 7$ gives the next term. In other words, $a_{n} = a_{1} r^{n - 1}$ .

Geometric Sequence: $r = - 7$

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 $r = - 7$ .

$a_{n} = 2 {(- 7)}^{n - 1}$

Step 4

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

$a_{6} = 2 {(- 7)}^{(6) - 1}$

Step 5

Subtract $1$ from $6$ .

$a_{6} = 2 {(- 7)}^{5}$

Step 6

Raise $- 7$ to the power of $5$ .

$a_{6} = 2 \cdot - 16807$

Step 7

Multiply $2$ by $- 16807$ .

$a_{6} = - 33614$

Find the 6th Term 2 , -14 , 98 , -686

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