# Grade FG Sequences and Rules Generate terms of

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Grade F/G Sequences and Rules Generate terms of a sequence from a term-to-term rule, including from patterns and diagrams If you have any questions regarding these resources or come across any errors, please contact helpful-report@pixl. org. uk

Key Vocabulary Sequence Term-to-term rule Arithmetic sequence Geometric sequence

Term-to-term Rules The term-to-term rule is the operation that is applied to one number in the sequence to generate the next number. Examples (a) The sequence 7, 7. 2, 7. 4, 7. 6, 7. 8. . . has a term-toterm rule of add 0. 2. (b) The sequence 40, 35, 30, 25, 20. . . . has a term-toterm rule of subtract 5. (c) The sequence 2, 4, 8, 16, 32. . . . has a term-to-term rule of multiply by 2. (d) The sequence 81, 27, 9, 3, 1. . . Has term-to-term of divide by 3. Sequences a & b are arithmetic and c & d are geometric

Now you try: Write down the term-to-term rules for these sequences. a) 2. 3, 2. 9, 3. 5, 4. 1, 4. 7 add 0. 6 b) 10, 9. 7, 9. 4, 9. 1, 8. 8 subtract 0. 3 multiply by 5 c) 0. 4, 2, 10, 50, 250 d) 200, 100, 50, 25, 12. 5 divide by 2 e) 1, 4, 10, 22, 46 multiply by 2 then add 2 or +3, + 6, + 12 + 24 and double how much you add each time

Term-to-term Rule From Patterns Look at these shapes made from squares Shape 1 Shape 2 Shape 3 Shape 4 (a) Draw the 4 th shape. (b) Complete the table Shape No 1 2 3 4 5 No of squares 6 8 10 12 14 (c) Write down the term-to-term rule Term-to-term rule is add 2 more squares

Problem Solving and Reasoning Colin is thinking of an arithmetic sequence. His 2 nd term is 9 and his 5 th term is 30. What are the values of the 1 st, 3 rd and 4 th terms? +21 2 9, ___, 23 30 16 ___, 21 ÷ 3 = 7 +7 +7 +7

Problem Solving and Reasoning The rule for a sequence is add c and then multiply by 4 The second term is 16 and the third term is 88. Work out the first and fourth term. – 2 16, 88, 376 ___, ___ We need to find the value of c. Using inverse operations 88 ÷ 4 = 22 22 – 16 = 6 c=6 (88 + 6) x 4 = 376 16 ÷ 4 – 6 = – 2

Problem Solving and Reasoning A sequence has term-to-term rule multiply by 3 then add 5. The 2 nd term is 11. (a) What are the values of the 1 st and 3 rd terms? (b) The 8 th term is 9, 839. Use this information to find the value of the 7 th term. Solution (a) 3 rd term = 11 x 3 + 5 = 38 1 st term = (11 – 5) ÷ 3 = 2 Solution (b) 7 th term = (9, 839 – 5) ÷ 3 = 3, 278