Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Woo-Jin and Kiran were asked to find an explicit formula for the sequence $64, 16, 4, 1$ , where the first term should be $f(1)$

View step-by-step help

View step-by-step help

Simplify radical expressions with variables II

Full solution

Q. Woo-Jin and Kiran were asked to find an explicit formula for the sequence

64, 16, 4, 1

, where the first term should be

f(1)

Identify Geometric Pattern: We observe that each term in the sequence is the previous term divided by $4$ . This suggests that the sequence is geometric with the first term $a = 64$ and the common ratio $r = \frac{1}{4}$ .
Find Explicit Formula: To find the explicit formula for a geometric sequence, we use the formula $f(n) = a \cdot r^{(n-1)}$ , where $a$ is the first term, $r$ is the common ratio, and $n$ is the term number.
Substitute Values: Substitute the values of $a$ and $r$ into the formula to get $f(n) = 64 \times (\frac{1}{4})^{(n-1)}$ .
Simplify Formula: We can simplify the formula by noting that $64$ is $4^3$ , so we can write the formula as $f(n) = 4^3 \times (\frac{1}{4})^{(n-1)}$ .
Apply Exponent Property: Using the property of exponents that $(a^m)^n = a^{m*n}$ , we can simplify the formula further to $f(n) = 4^{3-n+1}$ .
Final Explicit Formula: Simplify the exponent to get the final explicit formula: $f(n) = 4^{4-n}$ .

More problems from Simplify radical expressions with variables II

Question

Find the real-number root.

\newline

\sqrt{16}

\newline

\newline

Write your answer in simplified form.

\newline

\_\_\_\_

Posted 2 months ago

Question

Find the real-number root.

\newline

\sqrt{\frac{9}{16}}

\newline

Simplify your answer and write it as a decimal or as a proper or improper fraction.

\newline

\_\_\_\_\_

Posted 2 months ago

Question

Find the real-number root using a calculator. Round your answer to the nearest thousandth.

\newline

\newline

Posted 2 months ago

Question

Multiply. Write your answer in simplest form.

\newline

\sqrt{273} \times \sqrt{42}

\newline

Posted 1 month ago

Question

\newline

\sqrt{\frac{63}{4}}

\newline

Posted 2 months ago

Question

Simplify. Rationalize the denominator.

\newline

\frac{-4}{9 - \sqrt{2}}

\newline

Posted 2 months ago

Question

z

\newline

16 = \sqrt{z}

\newline

z =

Posted 2 months ago

Question

Simplify the radical expression.

\sqrt{14x^{14}}

Write your answer in the form

A

\sqrt{B}

A\sqrt{B}

A

B

are constants or expressions in

x

. Use at most one radical in your answer, and at most one absolute value symbol in your expression for

A

Posted 2 months ago

Question

Simplify the radical expression.

\newline

\sqrt{12x^{12}}

\newline

Write your answer in the form

A

\sqrt{B}

A\sqrt{B}

A

B

are constants or expressions in

x

. Use at most one radical in your answer, and at most one absolute value symbol in your expression for

A

\newline

\underline{\hspace{3cm}}

Posted 2 months ago

Question

What is the value of

\sin \left(\frac{5 \pi}{6}\right) ?

\newline

1

\newline

-\frac{\sqrt{3}}{2}

\newline

-\frac{\sqrt{2}}{2}

\newline

\frac{1}{2}

\newline

150

Posted 4 months ago