2.3.2 Recognizing, arithmetic and geometric sequences

• The 5th term of the arithmetic sequence 2, 5, 8, 11... is 14.


  True
• What is the value of \( n \) in the example used to find the 5th term?

  5
• What is a geometric sequence?

  Terms multiplied by ratio
• Arithmetic sequences can only increase in value.

  False
• What is the common difference in the arithmetic sequence 5, 8, 11, 14?

  3
• Steps to find the common difference in an arithmetic sequence

  1️⃣ Pick any two consecutive numbers in the sequence

  2️⃣ Subtract the first number from the second number
• Match the symbol with its meaning:

  \( a_n \) ↔️ The term we want to find

  \( a_1 \) ↔️ The first term in the sequence

  \( n \) ↔️ The term number we want

  \( d \) ↔️ The common difference
• The variable \( n \) in the nth term formula represents the term number.


  True
• What does the common difference in an arithmetic sequence describe?

  The amount added or subtracted
• What is the common ratio in a geometric sequence?

  The number multiplied
• What is the common ratio in the geometric sequence 3, 6, 12, 24?


  2
• In a geometric sequence, each term is multiplied by the same number.


  True
• The common ratio is always a whole number.

  False
• Steps to identify the common ratio in a geometric sequence

  1️⃣ Choose two consecutive terms

  2️⃣ Divide the second term by the first term

  3️⃣ The result is the common ratio
• What does \( a_n \) represent in the formula for the nth term of an arithmetic sequence?

  The nth term
• The symbol \( a_n \) refers to the term we want to find in an arithmetic sequence.


  True
• What is an arithmetic sequence?

  Numbers with a constant difference
• What does \( a_1 \) represent in the formula for the nth term of a geometric sequence?

  The first term
• What does \( d \) stand for in the formula for the nth term of an arithmetic sequence?

  The common difference
• Steps to find the 5th term of the geometric sequence 3, 6, 12, 24...

  1️⃣ Identify \( a_1 \), \( r \), and \( n \)

  2️⃣ Substitute the values into the formula

  3️⃣ Calculate the exponent

  4️⃣ Multiply to find \( a_5 \)
• In the sequence 3, 6, 12, 24..., what is the value of \( a_1 \)?

  3
• In an arithmetic sequence, each term changes by the same constant amount.


  True
• The term number in the formula for the nth term of a geometric sequence is represented by \( n \).

  True
• What is the 5th term of the geometric sequence 3, 6, 12, 24...?

  48
• What is the 5th term of the geometric sequence 3, 6, 12, 24...?

  48
• Geometric sequences use multiplication, while arithmetic sequences use addition.


  True