Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

The first three terms of a sequence are given. Write your answer as a decimal or whole number. Round to the nearest thousandth (if necessary).

14,28,56,dots
Find the 6th term.
Answer:

The first three terms of a sequence are given. Write your answer as a decimal or whole number. Round to the nearest thousandth (if necessary). $\newline$ $14,28,56, \ldots$ $\newline$ Find the $6$ th term. $\newline$ Answer:

View step-by-step help

View step-by-step help

Powers with decimal bases

Full solution

Q. The first three terms of a sequence are given. Write your answer as a decimal or whole number. Round to the nearest thousandth (if necessary).

\newline

14,28,56, \ldots

\newline

Find the

6

th term.

\newline

Answer:

Identify Pattern: Identify the pattern in the sequence. $\newline$ The given sequence is $14$ , $28$ , $56$ . We notice that each term is double the previous term. $\newline$ $14 \times 2 = 28$ $\newline$ $28 \times 2 = 56$ $\newline$ This is a geometric sequence with a common ratio of $2$ .
Use Formula: Use the formula for the $n$ th term of a geometric sequence. $\newline$ The $n$ th term of a geometric sequence is given by $a_n = a_1 \cdot r^{(n-1)}$ , where $a_1$ is the first term, $r$ is the common ratio, and $n$ is the term number. $\newline$ For this sequence, $a_1 = 14$ and $r = 2$ .
Calculate $6$ th Term: Calculate the $6$ th term using the formula. $\newline$ $a_6 = 14 \times 2^{6-1}$ $\newline$ $a_6 = 14 \times 2^5$ $\newline$ $a_6 = 14 \times 32$ $\newline$ $a_6 = 448$

More problems from Powers with decimal bases

Question

Write the expression using an exponent.

\newline

2 \times 2

\newline

Posted 2 months ago

Question

Evaluate the expression.

4 - 4^2

Posted 2 months ago

Question

x^2 = 4

Posted 1 month ago

Question

x^2 = 9

Posted 3 months ago

Question

\newline

x^2 = 0

\newline

Write your answer in simplified, rationalized form.

\newline

x =

x =

Posted 3 months ago

Question

x

\newline

8 = 2^x

\newline

x =

Posted 3 months ago

Question

x

\newline

6 = 7^x

\newline

x =

Posted 3 months ago

Question

Select the equivalent expression.

\newline

((8^{-5})/(2^{-2}))^{-4}=?

\newline

1

\newline

\newline

(8^{20})/(2^{8})

\newline

\newline

(2^{6})/(8^{9})

\newline

\newline

(1)/(8\cdot 2^{2})

Posted 4 days ago

Question

Select the equivalent expression.

\newline

\left(\frac{b^{7}}{4^{5}}\right)^{-3}=\,?

\newline

1

\newline

\frac{b^{21}}{4^{15}}

\newline

\frac{4^{15}}{b^{21}}

\newline

b^{-21}\cdot 4^{-15}

Posted 1 month ago

Question

Select the equivalent expression.

\newline

(3^{3}\cdot6^{6})^{-3}=

\newline

1

\newline

\frac{1}{3^{9}\cdot6^{18}}

\newline

\frac{6^{18}}{3^{9}}

\newline

\frac{3^{9}}{6^{18}}

Posted 1 month ago