58 nth B1 2 B1 for obtaining the difference of 5 M The difference is 5 so term is 5n + c c where = first term 5 M1 c – M1 for finding A1 A1 cao = 4 5 = – –1 A1 nth A1 cao So term is 5n 1. – Check the 4th term gives 19. n When = 4, 4n 1 = 20 1 = 19, – – B1 B1 for showing a check works correct. 5 59 B1 2 B1 for showing triangular numbers M Triangular numbers are 1, 3, 6, 10, 15 3 ….. This will give a table as: M1 M1 for method of finding differences A1 A1 for correct table B1 B1 for explanation of extending table backwards Extending the table backwards will a, b c allow us to find the values of and M1 M1 for method of extending table nth an2 bn c. in the term + + A1 A1 for correct table . a 2a = 1 = → B1 a B1 correct B1 a b b + = 1 = b → B1 correct B1 c c B1 correct = 0 nth n2 n n) Hence term is + = (n2 + n(n = + 1) B1 B1 for correct evaluation of generalisation to show given result 10
58 The difference is 5 so nth term is 5n + c where c = first term – 5 = 4 – 5 = –1 So nth term is 5n – 1. Check the 4th term gives 19. When n = 4, 4n – 1 = 20 – 1 = 19, correct. B1 M1 A1 A1 B1 2 B1 for obtaining the difference of 5 M1 for finding c A1 cao A1 cao B1 for showing a check works M 5 59 Triangular numbers are 1, 3, 6, 10, 15 ….. This will give a table as: Extending the table backwards will allow us to find the values of a, b and c in the nth term an2 + bn + c. . 2a = 1 → a = a + b = 1 → b = c = 0 Hence nth term is n2 + n = (n2 + n) = n(n + 1) B1 M1 A1 B1 M1 A1 B1 B1 B1 B1 2 3 B1 for showing triangular numbers M1 for method of finding differences A1 for correct table B1 for explanation of extending table backwards M1 for method of extending table A1 for correct table B1 correct a B1 correct b B1 correct c B1 for correct evaluation of generalisation to show given result M 10
Higher_Skills_Algebra_MarkScheme_AQA.docx