Algebra Examples

$6$ , $30$ , $150$ , $750$

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: $r = 5$

This is the form of a geometric sequence.

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

Substitute in the values of $a_{1} = 6$ and $r = 5$ .

$a_{n} = 6 \cdot 5^{n - 1}$

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

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

Subtract $1$ from $6$ .

$a_{6} = 6 \cdot 5^{5}$

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

$a_{6} = 6 \cdot 3125$

Multiply $6$ by $3125$ .

$a_{6} = 18750$