Find the 4th Term 250 , 50 , 10

$250$ , $50$ , $10$

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

Geometric Sequence: $r = \frac{1}{5}$

Step 2

This is the form of a geometric sequence.

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

Step 3

Substitute in the values of $a_{1} = 250$ and $r = \frac{1}{5}$ .

$a_{n} = 250 {(\frac{1}{5})}^{n - 1}$

Step 4

Apply the product rule to $\frac{1}{5}$ .

$a_{n} = 250 \frac{1^{n - 1}}{5^{n - 1}}$

Step 5

One to any power is one.

$a_{n} = 250 \frac{1}{5^{n - 1}}$

Step 6

Combine $250$ and $\frac{1}{5^{n - 1}}$ .

$a_{n} = \frac{250}{5^{n - 1}}$

Step 7

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

$a_{4} = \frac{250}{5^{(4) - 1}}$

Step 8

Simplify the denominator.

Subtract $1$ from $4$ .

$a_{4} = \frac{250}{5^{3}}$

Raise $5$ to the power of $3$ .

$a_{4} = \frac{250}{125}$

Step 9

Divide $250$ by $125$ .

$a_{4} = 2$

Find the 4th Term 250 , 50 , 10

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