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Sequences – Mixed – Foundation – GCSE Questions – AQA

Practice identifying arithmetic, geometric, Fibonacci, triangular, cube, and square sequences. Solve questions similar to AQA GCSE exams. Worksheets in printable sizes. Learn to identify sequence types and rules.

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Sequences – Mixed – Foundation – GCSE Questions – AQA

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  1. Sequences – Mixed – Foundation – GCSE Questions – AQA These questions are the same format as previous GCSE exams. COPY means they use the exact same numbers as the original GCSE question. Otherwise, they are clonequestions using different numbers. The worksheets are provided in 2 sizes.

  2. Printing To print handouts from slides - Select the slide from the left. Then click: File > Print > ‘Print Current Slide’ To print multiple slides - Click on a section title to highlight all those slides, or press ‘Ctrl’ at the same time as selecting slides to highlight more than one. Then click: File > Print > ‘Print Selection’ To print double-sided handouts - Highlight both slides before using ‘Print Selection’. Choose ‘Print on Both Sides’ and ‘Flip on Short Edge’.

  3. AQA Foundation: June 2018 Paper 2, Q23 AQA Foundation: June 2018 Paper 2, Q23 1 Match each sequence to its description. One has been done for you. 1 Match each sequence to its description. One has been done for you. [4 marks] [4 marks] 1 1 2 3 5 8 Arithmetic progression 1 1 2 3 5 8 Arithmetic progression 1 2 4 8 16 32 Geometric progression 1 2 4 8 16 32 Geometric progression 1 2 3 4 5 6 Fibonacci sequence 1 2 3 4 5 6 Fibonacci sequence 1 3 6 10 15 21 Triangular numbers 1 3 6 10 15 21 Triangular numbers 1 4 9 16 25 36 Cube numbers 1 4 9 16 25 36 Cube numbers 1 8 27 64 125 216 Square numbers 1 8 27 64 125 216 Square numbers AQA Foundation: June 2018 Paper 2, Q23 AQA Foundation: June 2018 Paper 2, Q23 1 Match each sequence to its description. One has been done for you. 1 Match each sequence to its description. One has been done for you. [4 marks] [4 marks] 1 1 2 3 5 8 Arithmetic progression 1 1 2 3 5 8 Arithmetic progression 1 2 4 8 16 32 Geometric progression 1 2 4 8 16 32 Geometric progression 1 2 3 4 5 6 Fibonacci sequence 1 2 3 4 5 6 Fibonacci sequence 1 3 6 10 15 21 Triangular numbers 1 3 6 10 15 21 Triangular numbers 1 4 9 16 25 36 Cube numbers 1 4 9 16 25 36 Cube numbers 1 8 27 64 125 216 Square numbers 1 8 27 64 125 216 Square numbers

  4. AQA Foundation: June 2017 Paper 2, Q15 AQA Foundation: June 2017 Paper 2, Q15 1 Here are some numbers. 1 Here are some numbers. 4 8 9 14 20 24 4 8 9 14 20 24 4 9 14 is an arithmetic progression. Use three of the numbers to make a different arithmetic progression. Describe the rule. 4 9 14 is an arithmetic progression. Use three of the numbers to make a different arithmetic progression. Describe the rule. [2 marks] [2 marks] Answer Answer Rule Rule AQA Foundation: June 2017 Paper 2, Q15 AQA Foundation: June 2017 Paper 2, Q15 1 Here are some numbers. 1 Here are some numbers. 4 8 9 14 20 24 4 8 9 14 20 24 4 9 14 is an arithmetic progression. Use three of the numbers to make a different arithmetic progression. Describe the rule. 4 9 14 is an arithmetic progression. Use three of the numbers to make a different arithmetic progression. Describe the rule. [2 marks] [2 marks] Answer Answer Rule Rule

  5. AQA Foundation: June 2017 Paper 2, Q4 AQA Foundation: June 2017 Paper 2, Q4 1 Here is a sequence. 57 52 47 42 37 Circle the expression for the th term of the sequence. 1 Here is a sequence. 57 52 47 42 37 Circle the expression for the th term of the sequence. [1 mark] [1 mark] − 5 5+ 62 62 − 5 5+ 52 − 5 5+ 62 62 − 5 5+ 52 2 Here is a sequence. −33 −25 −17 −9 −1 Circle the expression for the th term of the sequence. 2 Here is a sequence. −33 −25 −17 −9 −1 Circle the expression for the th term of the sequence. [1 mark] [1 mark] 8− 41 8− 33 −33 + 8 41 − 8 8− 41 8− 33 −33 + 8 41 − 8 AQA Foundation: June 2017 Paper 2, Q4 AQA Foundation: June 2017 Paper 2, Q4 1 Here is a sequence. 57 52 47 42 37 Circle the expression for the th term of the sequence. 1 Here is a sequence. 57 52 47 42 37 Circle the expression for the th term of the sequence. [1 mark] [1 mark] − 5 5+ 62 62 − 5 5+ 52 − 5 5+ 62 62 − 5 5+ 52 2 Here is a sequence. −33 −25 −17 −9 −1 Circle the expression for the th term of the sequence. 2 Here is a sequence. −33 −25 −17 −9 −1 Circle the expression for the th term of the sequence. [1 mark] [1 mark] 8− 41 8− 33 −33 + 8 41 − 8 8− 41 8− 33 −33 + 8 41 − 8

  6. AQA Foundation: June 2018 Paper 3, Q29 AQA Foundation: June 2018 Paper 3, Q29 1 The th term of a sequence is 12– 5 Work out the numbers in the sequence that have two digits and are not prime. 1 The th term of a sequence is 12– 5 Work out the numbers in the sequence that have two digits and are not prime. [3 marks] [3 marks] Answer Answer AQA Foundation: June 2018 Paper 3, Q29 AQA Foundation: June 2018 Paper 3, Q29 1 The th term of a sequence is 12– 5 Work out the numbers in the sequence that have two digits and are not prime. 1 The th term of a sequence is 12– 5 Work out the numbers in the sequence that have two digits and are not prime. [3 marks] [3 marks] Answer Answer

  7. AQA Foundation: November 2017 Paper 1, Q17 AQA Foundation: November 2017 Paper 1, Q17 1 A sequence has three terms. The term-to-term rule for the sequence is 1 A sequence has three terms. The term-to-term rule for the sequence is multiply by 8 and then add 11 multiply by 8 and then add 11 The first term of the sequence is –1 Work out the third term. The first term of the sequence is –1 Work out the third term. 1 (a) 1 (a) [2 marks] [2 marks] Answer Answer 1 (b) 1 (b) The order of the three terms is reversed to make a new sequence. Work out the term-to-term rule for this sequence. The order of the three terms is reversed to make a new sequence. Work out the term-to-term rule for this sequence. [1 mark] [1 mark] Answer Answer

  8. AQA Foundation: November 2017 Paper 2, Q28 AQA Foundation: November 2017 Paper 2, Q28 1 Work out the next term of this quadratic sequence. 1 Work out the next term of this quadratic sequence. [2 marks] [2 marks] 4 6 13 27 … 4 6 13 27 … Answer Answer AQA Foundation: November 2017 Paper 2, Q28 AQA Foundation: November 2017 Paper 2, Q28 1 Work out the next term of this quadratic sequence. 1 Work out the next term of this quadratic sequence. [2 marks] [2 marks] 4 6 13 27 … 4 6 13 27 … Answer Answer

  9. AQA Foundation: June 2018 Paper 3, Q22 AQA Foundation: June 2018 Paper 3, Q22 1 Here is a rule for a sequence. 1 Here is a rule for a sequence. After the first two terms, each term is half the sum of the previous two terms After the first two terms, each term is half the sum of the previous two terms 1 (a) Here is a sequence that follows this rule. 1 (a) Here is a sequence that follows this rule. 2 10 6 ….. ….. ….. 2 10 6 ….. ….. ….. Show that the 6th term is the first one that is not a whole number. Show that the 6th term is the first one that is not a whole number. [3 marks] [3 marks] 1 (b) A different sequence follows the same rule. 1 (b) A different sequence follows the same rule. The 1st term is 4 The 3rd term is 9.5 The 1st term is 4 The 3rd term is 9.5 4 ….. 9.5 4 ….. 9.5 [3 marks] [3 marks] Work out the 2nd term. Work out the 2nd term. Answer Answer

  10. AQA Foundation: November 2017 Paper 1, Q17 1 A sequence has three terms. The term-to-term rule for the sequence is multiply by 8 and then add 11 The first term of the sequence is –1 Work out the third term. 1 (a) [2 marks] Answer 1 (b) The order of the three terms is reversed to make a new sequence. Work out the term-to-term rule for this sequence. [1 mark] Answer

  11. AQA Foundation: June 2018 Paper 3, Q22 1 Here is a rule for a sequence. After the first two terms, each term is half the sum of the previous two terms 1 (a) Here is a sequence that follows this rule. 2 10 6 ….. ….. ….. Show that the 6th term is the first one that is not a whole number. [3 marks] 1 (b) A different sequence follows the same rule. The 1st term is 4 The 3rd term is 9.5 4 ….. 9.5 [3 marks] Work out the 2nd term. Answer

  12. AQA Foundation: November 2017 Paper 1, Q17 1 A sequence has three terms. The term-to-term rule for the sequence is multiply by 8 and then add 11 The first term of the sequence is –1 Work out the third term. 1 (a) [2 marks] 1st −1 −1 × 8 + 11 = 3 2nd 3 × 8 + 11 = 35 3rd 35 Answer 1 (b) The order of the three terms is reversed to make a new sequence. Work out the term-to-term rule for this sequence. [1 mark] 35 3 −1 Reverse operations Subtract 11, divide by 8 Answer

  13. AQA Foundation: June 2018 Paper 3, Q22 1 Here is a rule for a sequence. After the first two terms, each term is half the sum of the previous two terms 1 (a) Here is a sequence that follows this rule. 8 7 7.5 2 10 6 ….. ….. ….. Show that the 6th term is the first one that is not a whole number. [3 marks] 4th : 6th : 5th : 1 (b) A different sequence follows the same rule. The 1st term is 4 The 3rd term is 9.5 4 ….. 9.5 [3 marks] 9.5 = Work out the 2nd term. 19 = 15 = Answer

  14. Questions? Comments? Suggestions? …or have you found a mistake!? Any feedback would be appreciated . Please feel free to email: tom@goteachmaths.co.uk

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