1, 7, 13, 19, 25, ...

1. (a)1, 7, 13, 19, 25, ...
2. (a)(i)Find an expression, in terms of n, for the nth term of this sequence.[2]
3. (a)(ii)Explain why 251 is not a term in this sequence.[1]
4. (b)Here is another sequence. 5, 8, 13, 20, 29, ... The pth term of this sequence is p² + 4. Write down an expression, in terms of p, for the pth term of these sequences.
5. (b)(i)2, 1, 6, 13, 22, ...[1]
6. (b)(ii)7, 12, 19, 28, 39, ...[1]
7. (c)The diagrams below show the first three patterns in a sequence. The patterns are made from short diagonal lines.
8. (c)(i)Draw Pattern 4 on the dotty grid below.[1]
9. (c)(ii)Complete the table below for the number of short lines in Patterns 4 and 5. Pattern 1 2 3 4 5 Number of short lines 4 10 18[2]
10. (c)(iii)Find an expression, in terms of t, for the number of short lines in Pattern t.[2]

This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.