4n3Count in 4’s to give the 4 times table: 4,  8,  12,  16,  20, …  80,  84,  88,  …

Now shift the 4 times table up 3 to give 7,  11, 15,  19,  23, … 83,  87,  91,  …

Which tables were shifted to give the following sequences? By how much? Explain how you know.

(a) 7,  12,  17,  22, 27, …  82,  87,  92,  …

(b) 9,  11,  13,  15,  17, … 89,  91,  93, …

(c) 13,  20,  27,  34,  41, …  83,  90, 97, …

(d) 4,  7,  10,  13,  16,  …   79, 82, 85, …

(e) 5,  11,  17,  23,  29, …  71,  77,  83, …

Match each of the following rules for mapping n = 1, 2, 3 … to numbers in the sequences above. Explain how you do this.

(1) \(n\to 7n+6\)

(2) \(n\to 5n+2\)

(3)  \(n\to 3n+1\)

(4) \(n\to 6n-1\)

(5) \(n\to 2n+7\)

Now make up your own sequence and rule.

Click here for Notes for Teachers.

This problem is adapted from the NRICH task Shifting Times Tables with permission of the University of Cambridge. All rights reserved.

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