2.3.3 Finding the nth term of linear and quadratic sequences

• How do you calculate the 5th term (a_5) in the sequence 3, 5, 7, 9, ...?

  $a_{5} =$$3 +$$(5 - 1) \times 2$
• The 5th term in the sequence 3, 5, 7, 9, ... is 11.


  True
• The difference between terms in a quadratic sequence is constant.

  False
• What happens to the numbers in a linear sequence with each term?

  They increase or decrease by the same fixed number
• Match the property with its description:

  Second difference ↔️ Constant value

  First difference ↔️ Varying value

  Graph ↔️ Curved line
• What is the second difference in the example sequence 1, 4, 9, 16, 25?


  2
• What indicates that a sequence is quadratic?

  Constant second difference
• If you plot the numbers in a linear sequence on a graph, they will form a straight line.


  True
• What is the first term in the sequence 3, 5, 7, 9, ...?


  3
• Match the term number with its value in the sequence 3, 5, 7, 9, 11, ...

  Term Number 1 ↔️ 3

  Term Number 2 ↔️ 5

  Term Number 3 ↔️ 7

  Term Number 4 ↔️ 9

  Term Number 5 ↔️ 11
• The first difference in the example sequence is calculated by subtracting consecutive terms.

  True
• A sequence is quadratic if its second differences are constant.


  True
• The common difference must be the same between all pairs of consecutive numbers in a linear sequence.


  True
• Steps to identify a quadratic sequence using the second difference method.

  1️⃣ Calculate the first difference

  2️⃣ Calculate the second difference

  3️⃣ Check if the second difference is constant
• The second difference in the sequence 1, 4, 9, 16, ... is 2.


  True
• What does a_{n}</latex> represent in the formula for a quadratic sequence?

  nth term
• What is the general formula for the nth term of a linear sequence?

  $a_{n} =$$a_{1} +$$(n - 1)d$
• The 10th term of the sequence 2, 5, 8, 11, ... is 29.


  True
• What is the key feature of a quadratic sequence that is used to identify it?

  Second difference
• What is the common difference in a linear sequence?

  The amount each number changes
• What does $d$ represent in the formula for a linear sequence?


  Common difference
• The common difference in a linear sequence is represented by 'd'.


  True
• What is the common difference in the sequence 3, 5, 7, 9, 11, ...?

  2
• Assuming $B =$$0$ and $C =$$0$ simplifies the formula to $a_{n} =$$n^{2}$.


  True
• What is the simplified formula for the nth term of the quadratic sequence 1, 4, 9, 16, ...?

  $a_{n} =$$n^{2}$
• Match the formula components with their values in the linear sequence example:

  $a_{1}$ ↔️ 2

  $n$ ↔️ 10

  $d$ ↔️ 3

  $a_{10}$ ↔️ 29
• What is the formula for finding the nth term of a quadratic sequence?

  $a_{n} =$$An^{2} +$$Bn +$$C$
• The 7th term of the quadratic sequence 1, 4, 9, 16, ... is 49.


  True