Identify the Sequence 4 , 6 , 9 , 13.5 , 20.25

$4$ , $6$ , $9$ , $13.5$ , $20.25$

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 $\frac{3}{2}$ gives the next term. In other words, $a_{n} = a_{1} r^{n - 1}$ .

Geometric Sequence: $r = \frac{3}{2}$

Step 2

This is the form of a geometric sequence.

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

Step 3

Substitute in the values of $a_{1} = 4$ and $r = \frac{3}{2}$ .

$a_{n} = 4 {(\frac{3}{2})}^{n - 1}$

Step 4

Apply the product rule to $\frac{3}{2}$ .

$a_{n} = 4 \frac{3^{n - 1}}{2^{n - 1}}$

Step 5

Combine $4$ and $\frac{3^{n - 1}}{2^{n - 1}}$ .

$a_{n} = \frac{4 \cdot 3^{n - 1}}{2^{n - 1}}$

Identify the Sequence 4 , 6 , 9 , 13.5 , 20.25

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