Find the 4th Term 400 , 200 , 100

$400$ , $200$ , $100$

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

Geometric Sequence: $r = \frac{1}{2}$

This is the form of a geometric sequence.

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

Substitute in the values of $a_{1} = 400$ and $r = \frac{1}{2}$ .

$a_{n} = (400) \cdot {(\frac{1}{2})}^{n - 1}$

Simplify the expression.

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Apply the product rule to $\frac{1}{2}$ .

$a_{n} = 400 \cdot \frac{1^{n - 1}}{2^{n - 1}}$

One to any power is one.

$a_{n} = 400 \cdot \frac{1}{2^{n - 1}}$

Combine $400$ and $\frac{1}{2^{n - 1}}$ .

$a_{n} = \frac{400}{2^{n - 1}}$

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

$a_{4} = \frac{400}{2^{(4) - 1}}$

Simplify the denominator.

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Subtract $1$ from $4$ .

$a_{4} = \frac{400}{2^{3}}$

Raise $2$ to the power of $3$ .

$a_{4} = \frac{400}{8}$

Divide $400$ by $8$ .

$a_{4} = 50$

Find the 4th Term 400 , 200 , 100

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