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      Expressing an arithmetic sequence

      Lesson details

      Learning outcome

      I can appreciate that any term in an arithmetic sequence can be expressed in terms of its position in the sequence.

      Key learning points

      1. The general term of a sequence is called the n^th term.
      2. The value of n tells you what position in the sequence the term has.
      3. The term number tells you the value of n.

      Keywords

      • N^th term - The n^th term of a sequence is the position of a term in a sequence where n stands for the term number.

      Common misconception

      That $$n$$ is a term in the sequence. That $$n=10$$ means 10 is in the sequence.

      Reiterate that $$n$$ is the term number. "$$n=10$$ means the 10th term. What is the 10th term number?"

      Teacher tip

      Ask questions like "In this sequence, 7, 14, 21, 28, 35 what term number is 28? What is the $$n$$ value for the term 28?"

      Licence

      This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0
      except where otherwise stated. See Oak's terms & conditions
      (Collection 2).

      Lesson video

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      Prior knowledge starter quiz

      6 Questions

      Q1.
      In sequences, a position-to-term rule describes what?

      Correct answer: How to generate the term from the term number
      How many terms there are in a sequence
      How many positions there are in a sequence

      Q2.
      Multiplying $$x$$ by 4 and subtracting 7 is most simply written as which expression?

      $$x \times 4 - 7$$
      $$x \times -7 + 4$$
      $$4 + x - 7$$
      Correct answer: $$4x - 7$$

      Q3.
      Which position-to-term rule satisfies this sequence?

      An image in a quiz
      Add 3 each time.
      Starts at 1 and counts up in 3.
      Multiply by 3 and add 1
      Correct answer: Multiply by 3 and subtract 2

      Q4.
      Which position-to-term rule links the pattern number to the number of squares?

      An image in a quiz
      Multiply the pattern number by 4.
      Correct answer: Multiply the pattern number by 3 then add 1.
      Add 3 to the pattern number.
      Multiply the pattern number by 3 then subtract 1.

      Q5.
      For the arithmetic sequence starting 1, 4, 7, 10, 13, ... the position-to-term rule is 'multiply by 3 and subtract 2'. What therefore, is the 100$$^\text{th}$$ term?

      300
      302
      Correct answer: 298
      98

      Q6.
      Substitute the value $$a=6$$ into the below expressions. Order the value of the expressions from highest to lowest.

      1 - $$3a-7$$
      2 - $$2a-3$$
      3 - $$7-a$$
      4 - $$17-3a$$

      6 Questions

      Q1.
      The $$n^\text{th}$$ term of a sequence is the position of a term in a sequence where $$n$$ stands for the term .

      Correct Answer: number, term number

      Q2.
      In sequences $$n=20$$ means what?

      20 is in our sequence.
      The sequence goes up 20 each term.
      Correct answer: The 20$$^\text{th}$$ term number.
      The sequence is our 20 times table.

      Q3.
      In this sequence when $$n=4$$ what is the term value?

      An image in a quiz
      4
      Correct answer: 10
      7
      1
      13

      Q4.
      In this sequence when $$T=4$$ what is the term number?

      An image in a quiz
      $$n=4$$
      Correct answer: $$n=2$$
      $$n=5$$
      $$T=2$$
      $$T=5$$

      Q5.
      What general rule links pattern number ($$n$$) to number of squares ($$T$$) in this case?

      An image in a quiz
      Correct answer: $$T = n \times 4 + 3$$
      $$T = n + 4$$
      $$T = n \times 4 - 1$$
      $$T = n + 3$$

      Q6.
      What general rule links pattern number ($$n$$) to the perimeter of each shape?

      An image in a quiz
      $$+2$$
      $$n + 2$$
      $$12, 14, 16,\;$$...
      $$n \times 4$$
      Correct answer: $$n \times 2 + 10$$

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