Trigonometry Examples

$3$ , $7.5$ , $18.75$ , $46.875$ , $117.1875$ , $292.96875$ , $732.421875$ , $1831.0546875$ , $4577.63671875$

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 $2.5$ gives the next term. In other words, $a_{n} = a_{1} r^{n - 1}$ .

Geometric Sequence: $r = 2.5$

Step 2

This is the form of a geometric sequence.

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

Step 3

Substitute in the values of $a_{1} = 3$ and $r = 2.5$ .

$a_{n} = 3 \cdot {2.5}^{n - 1}$

Step 4

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

$a_{10} = 3 \cdot {2.5}^{(10) - 1}$

Step 5

Subtract $1$ from $10$ .

$a_{10} = 3 \cdot {2.5}^{9}$

Step 6

Raise $2.5$ to the power of $9$ .

$a_{10} = 3 \cdot 3814.69726562$

Step 7

Multiply $3$ by $3814.69726562$ .

$a_{10} = 11444.09179687$