2.3 Sequences

• In a geometric sequence, terms are multiplied by a common ratio.


  True
• An arithmetic sequence is defined by adding or subtracting a constant value called the common difference
• In the formula for an arithmetic sequence, `a_1` represents the first term of the sequence.
• In the formula for an arithmetic sequence, `a_1` represents the first term of the sequence.
• What is the formula for the nth term of an arithmetic sequence?

  $a_{n} =$$a_{1} +$$(n - 1)d$
• What is the formula for the nth term of an arithmetic sequence?

  $a_{n} =$$a_{1} +$$(n - 1)d$
• What is a sequence?

  Ordered list of numbers
• How is each term in a Fibonacci sequence calculated?

  Sum of two preceding terms
• How is the common difference in an arithmetic sequence calculated?

  $d =$$a_{n + 1} - a_{n}$
• Steps to find the nth term in an arithmetic sequence:

  1️⃣ Identify the first term (a_1)

  2️⃣ Calculate the common difference (d)

  3️⃣ Use the formula $a_{n} =$$a_{1} +$$(n - 1)d$
• Match the sequence type with its formula:

  Arithmetic ↔️ $a_{n} =$$a_{1} +$$(n - 1)d$

  Geometric ↔️ $a_{n} =$$a_{1} *$$r^{n - 1}$

  Fibonacci ↔️ $a_{n} =$$a_{n - 1} +$$a_{n - 2}$
• The nth term of an arithmetic sequence is given by the formula a_n = a_1 + (n-1)d
• In the arithmetic sequence 2, 5, 8, 11..., what is the common difference?

  3
• Match the property of arithmetic sequences with its description:

  Definition ↔️ Each term is obtained by adding or subtracting a common difference

  Common Difference ↔️ The constant amount added or subtracted between terms

  nth Term ↔️ The term at position n in the sequence
• The nth term of a geometric sequence is given by the formula a_n = a_1 * r^(n-1).


  True
• Match the property of geometric sequences with its description:

  Definition ↔️ Each term is obtained by multiplying the previous term by a common ratio

  Common Ratio ↔️ The constant amount each term is multiplied by

  nth Term ↔️ The term at position n in the sequence
• In the arithmetic sequence 2, 5, 8, 11..., what is the 10th term?

  29
• What is the defining characteristic of the Fibonacci sequence?

  Sum of the previous two terms
• The common difference in an arithmetic sequence is calculated by the formula d = a_(n+1) - a_n
• The nth term of a geometric sequence is given by the formula a_n = a_1 * r^(n-1).

  True
• What is the constant value called that is multiplied by each term in a geometric sequence?

  Common ratio
• What is the first term of the geometric sequence 3, 6, 12, 24...?

  3
• What is the common ratio of the geometric sequence 1, 4, 16, 64...?

  4
• In an arithmetic sequence, the common difference is the constant amount added or subtracted between terms
• The nth term formula for a geometric sequence is `a_n = a_1 * r^(n-1)`.
• Match the sequence type with its definition:

  Fibonacci sequence ↔️ Each term is the sum of the two preceding terms

  Arithmetic sequence ↔️ Terms increase by a common difference

  Geometric sequence ↔️ Terms are multiplied by a common ratio
• The nth term formula for an arithmetic sequence is `a_n = a_1 + (n-1)d`.
• Order the types of sequences from simplest to most complex based on their defining characteristic.

  1️⃣ Arithmetic sequences

  2️⃣ Geometric sequences

  3️⃣ Fibonacci sequences
• In an arithmetic sequence, terms increase or decrease by a common difference.


  True
• Match the sequence type with its common characteristic:

  Arithmetic ↔️ Common difference

  Geometric ↔️ Common ratio

  Fibonacci ↔️ Sum of previous terms
• In a geometric sequence, each term is obtained by multiplying the previous term by a common ratio.


  True
• The nth term formula for an arithmetic sequence is $a_{n} =$$a_{1} +$$(n - 1)d$
• What is a geometric sequence?

  Each term is multiplied
• Match the geometric sequence property with its description:

  Definition ↔️ Terms obtained by multiplying

  Common Ratio ↔️ Constant amount multiplied

  nth Term ↔️ Term at position n
• What is the nth term formula for an arithmetic sequence?

  $a_{n} =$$a_{1} +$$(n - 1)d$
• The first term in an arithmetic sequence is denoted by $a_{1}$


  True
• What is the formula for the sum of a geometric sequence?

  $S_{n} =$$\frac{a_{1}(r^{n} - 1)}{r - 1}$
• `r` is the common ratio
• A sequence is an ordered list of numbers or objects called terms
• What is the formula for the nth term of the Fibonacci sequence?

  $a_{n} =$$a_{n - 1} +$$a_{n - 2}$