Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Find the 11th term of the arithmetic sequence x+1,-5x+7,-11 x+13,dots Answer:

Find the 1111th term of the arithmetic sequence x+1,−5x+7,−11x+13,… x+1,-5 x+7,-11 x+13, \ldots \newlineAnswer:

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Find trigonometric functions using a calculatorright chevron icon

Full solution

Q. Find the 1111th term of the arithmetic sequence x+1,−5x+7,−11x+13,… x+1,-5 x+7,-11 x+13, \ldots \newlineAnswer:
  1. Determine common difference: To find the 11th11^{\text{th}} term of an arithmetic sequence, we need to determine the common difference between consecutive terms and then use the formula for the nthn^{\text{th}} term of an arithmetic sequence, which is an=a1+(n−1)da_n = a_1 + (n - 1)d, where ana_n is the nthn^{\text{th}} term, a1a_1 is the first term, nn is the term number, and dd is the common difference.
  2. Find common difference: First, let's find the common difference dd by subtracting the first term from the second term.d=(−5x+7)−(x+1)=−5x+7−x−1=−6x+6d = (-5x + 7) - (x + 1) = -5x + 7 - x - 1 = -6x + 6
  3. Verify common difference: Now, let's verify the common difference by subtracting the second term from the third term. \newlined=(−11x+13)−(−5x+7)=−11x+13+5x−7=−6x+6d = (-11x + 13) - (-5x + 7) = -11x + 13 + 5x - 7 = -6x + 6\newlineThis confirms that the common difference is indeed −6x+6-6x + 6.
  4. Find 1111th term: Using the formula for the nth term, we can now find the 1111th term a11a_{11}.a11=a1+(11−1)(−6x+6)=(x+1)+10(−6x+6)a_{11} = a_1 + (11 - 1)(-6x + 6) = (x + 1) + 10(-6x + 6)
  5. Simplify expression: Simplify the expression to find the 11th11^{\text{th}} term.a11=x+1+10(−6x)+10(6)=x+1−60x+60a_{11} = x + 1 + 10(-6x) + 10(6) = x + 1 - 60x + 60
  6. Combine like terms: Combine like terms to get the final expression for the 11th11^{th} term.a11=−59x+61a_{11} = -59x + 61

More problems from Find trigonometric functions using a calculator

Question
Find all solutions with 0∘≤θ≤180∘0^\circ \leq \theta \leq 180^\circ. Give the exact answer(s) in simplest form. If there are multiple answers, separate them with commas.\newlinecos⁡(θ)=−1\cos(\theta) = -1\newline‾∘\underline{\hspace{2em}}^\circ
Get tutor helpright-arrow

Posted 2 months ago

Question
Kimi's school is 1515 kilometers west of her house and 88 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_____\_\_\_\_\_ kilometers
Get tutor helpright-arrow

Posted 2 months ago

Question
Evaluate. Write your answer as an integer or as a decimal rounded to the nearest hundredth.\newlinecos⁡35∘=\cos 35^\circ = __
Get tutor helpright-arrow

Posted 2 months ago

Question
Find all solutions with −90∘≤θ≤90∘-90^\circ \leq \theta \leq 90^\circ. Give the exact answer(s) in simplest form. If there are multiple answers, separate them with commas.\newlinecsc⁡(θ)=−1\csc(\theta) = -1\newline____ ∘\_\_\_\_\,^\circ
Get tutor helpright-arrow

Posted 2 months ago

Question
Evaluate. Write your answer in simplified, rationalized form. Do not round.\newlinecot⁡30∘=\cot 30^\circ = ______
Get tutor helpright-arrow

Posted 2 months ago

Question
The terminal side of an angle θ\theta in standard position intersects the unit circle at (8485,1385)(\frac{84}{85}, \frac{13}{85}). What is cos⁡(θ)\cos(\theta)?\newlineWrite your answer in simplified, rationalized form.\newline______
Get tutor helpright-arrow

Posted 2 months ago

Question
−90∘<θ<90∘-90^\circ < \theta < 90^\circ. Find the value of θ\theta in degrees.\newlinetan⁡(θ)=0\tan(\theta) = 0\newlineWrite your answer in simplified, rationalized form. Do not round.\newlineθ=\theta = ____∘^\circ\newline
Get tutor helpright-arrow

Posted 2 months ago

Question
Evaluate. Write your answer in simplified, rationalized form. Do not round.\newlinecsc⁡60∘=\csc 60^\circ = ______
Get tutor helpright-arrow

Posted 2 months ago

Question
θ\theta is an acute angle. Find the value of θ\theta in degrees.\newlinesec⁡(θ)=2\sec(\theta) = \sqrt{2}\newlineθ=\theta = ____°\degree
Get tutor helpright-arrow

Posted 2 months ago

Question
Evaluate. Write your answer in simplified, rationalized form. Do not round.\newlinecos⁡90∘=\cos 90^\circ = ____
Get tutor helpright-arrow

Posted 3 months ago

View all (275)