Sequences – Linear – Foundation – GCSE Questions 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 clone questions using different numbers. The worksheets are provided in a variety of sizes.

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GCSE GCSE GCSE GCSE Edexcel Foundation: November 2017 Paper 3, Q18 Here is a sequence of patterns made with buttons. 1 Here is a sequence of patterns made with buttons. pattern number 1 pattern number 2 pattern number 3 pattern number 1 pattern number 2 pattern number 3 Find an expression, in terms of n, for the number of counters in pattern number n. Find an expression, in terms of n, for the number of counters in pattern number n. (2) (2) Abigail has 80 counter. (b) Can Abigail make a pattern in this sequence using all 80 of her counters? You must show how you get your answer. Abigail has 80 counter. (b) Can Abigail make a pattern in this sequence using all 80 of her counters? You must show how you get your answer. (2) (2) (Total for Question 1 is 4 marks) (Total for Question 1 is 4 marks) GCSE Edexcel Foundation: November 2017 Paper 3, Q18 GCSE Edexcel Foundation: November 2017 Paper 3, Q18 1 Here is a sequence of patterns made with buttons. 1 Here is a sequence of patterns made with buttons. pattern number 1 pattern number 2 pattern number 3 pattern number 1 pattern number 2 pattern number 3 Find an expression, in terms of n, for the number of counters in pattern number n. Find an expression, in terms of n, for the number of counters in pattern number n. (2) (2) Abigail has 80 counter. (b) Can Abigail make a pattern in this sequence using all 80 of her counters? You must show how you get your answer. Abigail has 80 counter. (b) Can Abigail make a pattern in this sequence using all 80 of her counters? You must show how you get your answer. (2) (2) (Total for Question 1 is 4 marks) (Total for Question 1 is 4 marks)

GCSE GCSE GCSE GCSE Edexcel Foundation: June 2017 Paper 2, Q25 Here are the first six terms of an arithmetic sequence. (a) Find an expression, in terms of n, for the nth term of this sequence. 1 Here are the first six terms of an arithmetic sequence. (a) Find an expression, in terms of n, for the nth term of this sequence. 2 6 10 14 18 2 6 10 14 18 The nth term of a different sequence is 4n2 Julie says that the 5th term of this sequence is 98 (b) Is Julie right? Show how you get your answer. (2) The nth term of a different sequence is 4n2 Julie says that the 5th term of this sequence is 98 (b) Is Julie right? Show how you get your answer. (2) (1) (1) (Total for Question 1 is 3 marks) (Total for Question 1 is 3 marks) GCSE Edexcel Foundation: June 2017 Paper 2, Q25 GCSE Edexcel Foundation: June 2017 Paper 2, Q25 1 Here are the first six terms of an arithmetic sequence. (a) Find an expression, in terms of n, for the nth term of this sequence. 1 Here are the first six terms of an arithmetic sequence. (a) Find an expression, in terms of n, for the nth term of this sequence. 2 6 10 14 18 2 6 10 14 18 The nth term of a different sequence is 4n2 Julie says that the 5th term of this sequence is 98 (b) Is Julie right? Show how you get your answer. (2) The nth term of a different sequence is 4n2 Julie says that the 5th term of this sequence is 98 (b) Is Julie right? Show how you get your answer. (2) (1) (1) (Total for Question 1 is 3 marks) (Total for Question 1 is 3 marks)

GCSE GCSE Edexcel Foundation: May 2017 Paper 1, Q11 A sequence of patterns is made from square tiles and triangular tiles. Here are the first three patterns in the sequence. 1 A sequence of patterns is made from square tiles and triangular tiles. Here are the first three patterns in the sequence. pattern number 1 pattern number 2 pattern number 3 pattern number 1 pattern number 2 pattern number 3 (a) How many square tiles are needed to make pattern number 7? (a) How many square tiles are needed to make pattern number 7? (2) (2) (b) How many triangular tiles are needed to make pattern number 22? (b) How many triangular tiles are needed to make pattern number 22? (2) (2) Anna says, “When the pattern number is odd, an odd number of square tiles is needed to make the pattern” (c) Is Anna right? You must give reasons for your answer. Anna says, “When the pattern number is odd, an odd number of square tiles is needed to make the pattern” (c) Is Anna right? You must give reasons for your answer. (2) (2) (Total for Question 1 is 6 marks) (Total for Question 1 is 6 marks)

GCSE GCSE Edexcel Foundation: June 2018 Paper 3, Q4 Here are the first 4 terms of a sequence. 3 9 15 21 (a) (i) Write down the next term in the sequence. (1) (ii) Explain how you got your answer. (1) (b) Work out the 10th term of the sequence. (1) (Total for Question 1 is 3 marks) GCSE Edexcel Foundation: June 2018 Paper 3, Q4 1 Here are the first 4 terms of a sequence. 3 9 15 21 (a) (i) Write down the next term in the sequence. (1) (ii) Explain how you got your answer. (1) (b) Work out the 10th term of the sequence. (1) (Total for Question 1 is 3 marks)

GCSE Edexcel Foundation: May 2017 Paper 1, Q11 A sequence of patterns is made from square tiles and triangular tiles. Here are the first three patterns in the sequence. pattern number 1 pattern number 2 pattern number 3 (a) How many square tiles are needed to make pattern number 7? (2) (b) How many triangular tiles are needed to make pattern number 22? (2) Anna says, “When the pattern number is odd, an odd number of square tiles is needed to make the pattern” (c) Is Anna right? You must give reasons for your answer. (2) (Total for Question 1 is 6 marks)

GCSE Edexcel Foundation: June 2018 Paper 3, Q4 1 Here are the first 4 terms of a sequence. 3 9 15 21 (a) (i) Write down the next term in the sequence. (1) (ii) Explain how you got your answer. (1) (b) Work out the 10th term of the sequence. (1) (Total for Question 1 is 3 marks)

GCSE Edexcel Foundation: November 2017 Paper 3, Q18 1 Here is a sequence of patterns made with buttons. pattern number 1 pattern number 2 pattern number 3 Find an expression, in terms of n, for the number of counters in pattern number n. 5, 9, 13 4, 8, 12 = 4n Need to add 1 4n + 1 4 times table (2) Abigail has 80 counter. (b) Can Abigail make a pattern in this sequence using all 80 of her counters? You must show how you get your answer. No, 80 buttons is not a pattern/number in this sequence. 4n + 1 = 80 4n = 79 n = 19.75 (2) (Total for Question 1 is 4 marks)

GCSE +4 +4 +4 +4 4n 4 8 12 16 20 4n - 2 substitute Edexcel Foundation: June 2017 Paper 2, Q25 1 Here are the first six terms of an arithmetic sequence. (a) Find an expression, in terms of n, for the nth term of this sequence. +4 +4 +4 +4 4n 2 6 10 14 18 4 8 12 16 20 must subtract 2 4n - 2 The nth term of a different sequence is 4n2 Julie says that the 5th term of this sequence is 98 (b) Is Julie right? Show how you get your answer. (2) substitute 4 x 52 = 4 x 25 = 100 Juie is wrong, the 5th term is 100. (1) (Total for Question 1 is 3 marks)

49 22 x 4 = 88 88 GCSE The rule for square tiles is n2. Edexcel Foundation: May 2017 Paper 1, Q11 1 A sequence of patterns is made from square tiles and triangular tiles. Here are the first three patterns in the sequence. pattern number 1 pattern number 2 pattern number 3 (a) How many square tiles are needed to make pattern number 7? pattern 1 2 3 4 5 6 7 Rule squares 9 16 25 36 49 Square triangles 8 12 20 24 28 x 4 49 (2) (b) How many triangular tiles are needed to make pattern number 22? 22 x 4 = 88 88 (2) Anna says, “When the pattern number is odd, an odd number of square tiles is needed to make the pattern” (c) Is Anna right? You must give reasons for your answer. The rule for square tiles is n2. If n is odd, then odd x odd must equal an odd number. Anna is correct because odd x odd is always odd. (2) (Total for Question 1 is 6 marks)

27 Increases by 6 each time OR 6n-3 57 GCSE Edexcel Foundation: June 2018 Paper 3, Q4 1 Here are the first 4 terms of a sequence. 3 9 15 21 (a) (i) Write down the next term in the sequence. 27 (1) (ii) Explain how you got your answer. Increases by 6 each time OR 6n-3 (1) (b) Work out the 10th term of the sequence. 57 (1) (Total for Question 1 is 3 marks)

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