Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Find the
15^("th ") term of the arithmetic sequence
5x+1,9x+7,13 x+13,dots
Answer:

Find the $15^{\text {th }}$ term of the arithmetic sequence $5 x+1,9 x+7,13 x+13, \ldots$ $\newline$ Answer:

View step-by-step help

View step-by-step help

Find trigonometric functions using a calculator

Full solution

Q. Find the

15^{\text {th }}

term of the arithmetic sequence

5 x+1,9 x+7,13 x+13, \ldots

\newline

Answer:

Determine Common Difference: To find the $15^{th}$ term of an arithmetic sequence, we need to determine the common difference between consecutive terms and then use the formula for the $n^{th}$ term of an arithmetic sequence, which is $a_n = a_1 + (n - 1)d$ , where $a_n$ is the $n^{th}$ term, $a_1$ is the first term, and $d$ is the common difference.
Find Common Difference: First, let's find the common difference $d$ by subtracting the first term from the second term: $(9x + 7) - (5x + 1) = 4x + 6$ . Then, subtract the second term from the third term: $(13x + 13) - (9x + 7) = 4x + 6$ . Since the difference is the same, the common difference $d$ is $4x + 6$ .
Use Formula for $15$ th Term: Now, we can use the formula to find the $15$ th term $a_{15}$ . The first term $a_1$ is $5x + 1$ . Plugging the values into the formula, we get $a_{15} = (5x + 1) + (15 - 1)(4x + 6)$ .
Simplify Expression: Simplify the expression: $a_{\(15\)} = (\(5\)x + \(1\)) + \(14\)(\(4\)x + \(6\)) = (\(5\)x + \(1\)) + (\(56\)x + \(84\)) = \(61\)x + \(85\).

More problems from Find trigonometric functions using a calculator

Question

Find all solutions with

0^\circ \leq \theta \leq 180^\circ

. Give the exact answer(s) in simplest form. If there are multiple answers, separate them with commas.

\newline

\cos(\theta) = -1

\newline

\underline{\hspace{2em}}^\circ

Posted 7 months ago

Question

Kimi's school is

15

kilometers west of her house and

8

kilometers south of her friend Franklin's house. Every day, Kimi bicycles from her house to her school. After school, she bicycles from her school to Franklin's house. Before dinner, she bicycles home on a bike path that goes straight from Franklin's house to her own house. How far does Kimi bicycle each day?

\newline

\_\_\_\_\_

Posted 7 months ago

Question

Evaluate. Write your answer as an integer or as a decimal rounded to the nearest hundredth.

\newline

\cos 35^\circ =

Posted 7 months ago

Question

Find all solutions with

-90^\circ \leq \theta \leq 90^\circ

. Give the exact answer(s) in simplest form. If there are multiple answers, separate them with commas.

\newline

\csc(\theta) = -1

\newline

\_\_\_\_\,^\circ

Posted 8 months ago

Question

Evaluate. Write your answer in simplified, rationalized form. Do not round.

\newline

\cot 30^\circ =

Posted 7 months ago

Question

The terminal side of an angle

\theta

in standard position intersects the unit circle at

(\frac{84}{85}, \frac{13}{85})

\cos(\theta)

\newline

Write your answer in simplified, rationalized form.

\newline

Posted 7 months ago

Question

-90^\circ < \theta < 90^\circ

. Find the value of

\theta

\newline

\tan(\theta) = 0

\newline

Write your answer in simplified, rationalized form. Do not round.

\newline

\theta =

^\circ

\newline

Posted 8 months ago

Question

Evaluate. Write your answer in simplified, rationalized form. Do not round.

\newline

\csc 60^\circ =

Posted 8 months ago

Question

\theta

is an acute angle. Find the value of

\theta

\newline

\sec(\theta) = \sqrt{2}

\newline

\theta =

\degree

Posted 7 months ago

Question

Evaluate. Write your answer in simplified, rationalized form. Do not round.

\newline

\cos 90^\circ =

Posted 8 months ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant