Find the 5th Term 3/20 , 3/2 , 15

$\frac{3}{20}$ , $\frac{3}{2}$ , $15$

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 $10$ gives the next term. In other words, $a_{n} = a_{1} r^{n - 1}$ .

Geometric Sequence: $r = 10$

Step 2

This is the form of a geometric sequence.

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

Step 3

Substitute in the values of $a_{1} = \frac{3}{20}$ and $r = 10$ .

$a_{n} = \frac{3}{20} \cdot 10^{n - 1}$

Step 4

Combine $\frac{3}{20}$ and $10^{n - 1}$ .

$a_{n} = \frac{3 \cdot 10^{n - 1}}{20}$

Step 5

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

$a_{5} = \frac{3 \cdot 10^{(5) - 1}}{20}$

Step 6

Simplify the numerator.

Subtract $1$ from $5$ .

$a_{5} = \frac{3 \cdot 10^{4}}{20}$

Raise $10$ to the power of $4$ .

$a_{5} = \frac{3 \cdot 10000}{20}$

Step 7

Simplify the expression.

Multiply $3$ by $10000$ .

$a_{5} = \frac{30000}{20}$

Divide $30000$ by $20$ .

$a_{5} = 1500$

Find the 5th Term 3/20 , 3/2 , 15

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