2.4 Sequences

• What is an arithmetic sequence?

  Constant difference between terms
• What are cube numbers in a sequence?

  Perfect cubes
• Arithmetic sequences have a constant difference
• In an arithmetic sequence, each term is obtained by adding a constant difference
• Order the steps to find the 10th term of the arithmetic sequence 2, 5, 8, 11, ...

  1️⃣ Identify $a_{1}$ and $d$

  2️⃣ Substitute into the formula $a_{n} =$$a_{1} +$$(n - 1)d$

  3️⃣ Simplify to find $a_{10}$
• In mathematics, a sequence is an ordered list of numbers or objects called terms
• What is the general formula for the nth term of an arithmetic sequence?

  $a_{n} =$$a_{1} +$$(n - 1)d$
• If the common difference is constant, the sequence is arithmetic


  True
• In the formula for the nth term of an arithmetic sequence, $a_{1}$ represents the first term.
• What is the formula for finding the nth term of a geometric sequence?

  $a_{n} =$$a_{1} \cdot r^{(n - 1)}$
• Steps to find the nth term of a geometric sequence

  1️⃣ Identify $a_{1}$ and $r$

  2️⃣ Substitute $a_{1}$, $r$, and $n$ into the formula

  3️⃣ Simplify the expression
• An arithmetic sequence is one where each term is obtained by adding a constant difference to the previous term.

  True
• The 10th term of the arithmetic sequence 2, 5, 8, 11, ... is 29.


  True
• What does $d$ represent in the arithmetic sequence formula?


  Constant difference
• The common difference in the arithmetic sequence 2, 5, 8, 11, ... is 3
• What is a sequence in mathematics defined as?

  Ordered list of terms
• Each term in a Fibonacci sequence is the sum of the two preceding terms.
• How is the common difference in an arithmetic sequence calculated?

  $a_{n} - a_{n - 1}$
• Steps to find the 10th term of the arithmetic sequence 2, 5, 8, 11, ...

  1️⃣ Identify $a_{1}$

  2️⃣ Identify $d$

  3️⃣ Plug into the formula $a_{n} =$$a_{1} +$$(n - 1)d$

  4️⃣ Simplify the equation
• In the sequence 2, 5, 8, 11, the first term $a_{1}$ is 2.
• The nth term of a geometric sequence can be found using the formula $a_{n} =$$a_{1} \cdot r^{(n - 1)}$, where $r$ is the common ratio.
• In the sequence 3, 6, 12, 24, the first term $a_{1}$ is 3.
• What is the defining characteristic of a linear sequence?

  Constant difference
• In a geometric sequence, each term is obtained by multiplying the previous term by a constant ratio
• Arithmetic sequences have a constant difference
• What is the general formula for the nth term of an arithmetic sequence?

  a_{n} = a_{1} + (n - 1)d</latex>
• In a geometric sequence, each term is obtained by multiplying the previous term by a constant ratio
• What is the value of $a_{1}$ in the arithmetic sequence 2, 5, 8, 11, ...?


  2
• Sequences can be either finite or infinite


  True
• In a geometric sequence, there is a constant ratio
• If the common ratio is constant, the sequence is geometric


  True
• $a_{1}$ in the formula for a geometric sequence represents the first
• The formula for the nth term of an arithmetic sequence is a_{n} = a_{1} + (n - 1)d</latex>
• What is an arithmetic sequence defined as?

  Adding a constant difference
• To solve arithmetic sequence problems, you need to identify the first term and the common difference.


  True
• What is the formula used to find the 10th term of the sequence 2, 5, 8, 11, ...?

  $a_{10} =$$2 +$$(10 - 1) \times 3$
• What type of sequence is 1, 4, 9, 16, 25, ...?

  Square numbers
• The nth term of an arithmetic sequence is denoted by $a_{n}$.
• What is the common difference in the arithmetic sequence 2, 5, 8, 11, ...?

  3
• What is the common ratio in the geometric sequence 3, 6, 12, 24, ...?

  2