Find the 6th Term 1 , -5 , 25 , -125

$1$ , $- 5$ , $25$ , $- 125$

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 $- 5$ gives the next term. In other words, $a_{n} = a_{1} r^{n - 1}$ .

Geometric Sequence: $r = - 5$

Step 2

This is the form of a geometric sequence.

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

Step 3

Substitute in the values of $a_{1} = 1$ and $r = - 5$ .

$a_{n} = 1 {(- 5)}^{n - 1}$

Step 4

Multiply ${(- 5)}^{n - 1}$ by $1$ .

$a_{n} = {(- 5)}^{n - 1}$

Step 5

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

$a_{6} = {(- 5)}^{(6) - 1}$

Step 6

Subtract $1$ from $6$ .

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

Step 7

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

$a_{6} = - 3125$

Find the 6th Term 1 , -5 , 25 , -125

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