Arithmetic Sequences Quiz: Formulas and Applications

Arithmetic sequence = A sequence with a common difference between consecutive terms Arithmetic mean = The average of two numbers 𝑛 𝑡ℎ term = The first term of an arithmetic sequence Common difference = The difference between two consecutive terms

𝑎𝑛 = 𝑎1 + (𝑛 - 1)𝑑 = Finding the 𝑛 𝑡ℎ term of an arithmetic sequence 𝑎𝑚 = (𝑎 + 𝑏) / 2 = Finding the arithmetic mean of two numbers 𝑑 = 𝑎𝑛 - 𝑎𝑛-1 = Finding the common difference of an arithmetic sequence 𝑎1 = 𝑎𝑛 - (𝑛 - 1)𝑑 = Finding the first term of an arithmetic sequence

Arithmetic sequence = Modeling real-world problems with a constant rate of change Arithmetic mean = Averaging grades in a class 𝑛 𝑡ℎ term = Finding the last term of a sequence Common difference = Determining the growth rate of a population

<p>2, 5, 8, 11, ... = Has a common difference of 3 10, 7, 4, 1, ... = Is a decreasing sequence -2, -2, -2, -2, ... = Has a constant term 1, 2, 4, 8, ... = Is a geometric sequence</p> Signup and view all the answers

<p>Find the 10th term of an arithmetic sequence = Finding the 𝑛 𝑡ℎ term of an arithmetic sequence Determine the arithmetic mean of 5 and 11 = Defining arithmetic means Find the common difference of an arithmetic sequence = Determining arithmetic means of a sequence Solve a real-world problem involving an arithmetic sequence = Solving problems involving 𝑛 𝑡ℎ term of an arithmetic sequence</p> Signup and view all the answers

<p>nth term = Find the unknown term of a sequence Arithmetic mean = Determine the middle value of a sequence Common difference = Find the difference between consecutive terms Arithmetic sequence = Define a sequence with a constant difference</p> Signup and view all the answers

<p>nth term = The general formula for the term in an arithmetic sequence Arithmetic mean = The middle value of a sequence Common difference = The constant difference between consecutive terms Arithmetic sequence = A sequence with a constant difference</p> Signup and view all the answers

<p>Finding the 10th term of a sequence = Writing a formula for the nth term Determining the common difference = Finding the nth term of a sequence Solving for an unknown term = Finding the arithmetic mean Finding the sum of a sequence = Determine the nth term of a sequence</p> Signup and view all the answers

<p>an = a1 + (n - 1)d = Find the nth term of a sequence am = (a1 + an)/2 = Determine the arithmetic mean d = an - an-1 = Find the common difference a1 + (n - 1)d = an = Find the first term of a sequence</p> Signup and view all the answers

<p>nth term formula = Finding the unknown term of a sequence Arithmetic mean formula = Determine the middle value of a sequence Common difference = Finding the difference between consecutive terms Arithmetic sequence definition = Defining a sequence with a constant difference</p> Signup and view all the answers