44 a a B1 2 a M is the first term. C1 for explaining B1 d d is the amount added each time. C1 for explaining b C1 a d C1 for creating a suitable example For example: use = 2 and = 3 to a generate the sequence in part as: C1 C1 for generating a value higher than the third term 2, 5, 8, 11, 14, … The 5th term is 14. P1 Xn P1 for showing the formula gives the same value Xn a Using the given = + (n - 1)d: the 5th term will be 2 + 4 × 3 = 14, the same value. c B1 B1 cao Xn arn-1 = d C1 C1 cao It is a quadratic sequence because it 7 n2. contains a term in 45 a Evidence of reproducing proof as given C1 2 C1 for correct proof clearly explained M in question. b = (2a + (n 1)d) Sn – a d for the set of integers, = 1 and = 1. a d C1 C1 for using and equal to 1 Hence = (2 + (n 1)) Sn – C1 C1 for correct substitution into the formula = (n + 1) P1 P1 for showing how this simplifies to the desired formula 4
44 a b c d a is the first term. d is the amount added each time. For example: use a = 2 and d = 3 to generate the sequence in part a as: 2, 5, 8, 11, 14, … The 5th term is 14. Using the given Xn = a + (n - 1)d: the 5th term will be 2 + 4 × 3 = 14, the same value. Xn = arn-1 It is a quadratic sequence because it contains a term in n2. B1 B1 C1 C1 P1 B1 C1 2 C1 for explaining a C1 for explaining d C1 for creating a suitable example C1 for generating a value higher than the third term P1 for showing the Xn formula gives the same value B1 cao C1 cao M 7 45 a b Evidence of reproducing proof as given in question. Sn = (2a + (n – 1)d) for the set of integers, a = 1 and d = 1. Hence Sn = (2 + (n – 1)) = (n + 1) C1 C1 C1 P1 2 C1 for correct proof clearly explained C1 for using a and d equal to 1 C1 for correct substitution into the formula P1 for showing how this simplifies to the desired formula M 4
Higher_Skills_Algebra_MarkScheme_Edexcel.docx