These are the first five terms of a sequence. 5 12 19 26 33 Find the next term of the sequence.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2023). The mark or mark type is shown in brackets.

1. [1] (a)(i) 40
2. [2] (a)(ii) 7n-2 oe final answer
3. [2] (a)(ii) B1 for 7n+j oe seen, j may be 0
4. [3] (a)(iii) 50
5. [3] (a)(iii) M1 for correct equation for sum of terms
6. [3] (a)(iii) FT use of their 7n-2
7. [3] (a)(iii) M1 for correct rearrangement to ak = b, dependent on equation with two terms in k and a constant Not k + k + 1 = 703 oe
8. [5] (b) 58
9. [5] (b) B4 for a=4 and b=-2
10. [5] (b) OR B2 for 1^2 + a + b = 3 or better and 3^2 + 3a + b = 19 or better or B1 for one correct
11. [5] (b) M1 for correct method to eliminate one variable from their simultaneous equations
12. [5] (b) M1 for 6^2 + their a x 6 + their b
13. [5] (b) Alternative method
14. [5] (b) B3 for second term = 10
15. [5] (b) OR B1 for second difference = 2
16. [5] (b) B2 for first pair of differences 7 and 9 or B1 for sum of first pair of differences = 16
17. [5] (b) AND B1 for next first differences 11, 13, 15