Liam is accumulating capital for a reforestation initiative over a span of 40 months. In the first month, he allocates £150 to the fund, and in each subsequent month, he increases this allocation by £6, so that he allocates £156 in the second month, £162 in the third month, and so on, forming an arithmetic sequence.
Find the amount Liam allocates in the 25th month. (2)
Calculate the total capital Liam accumulates over the full 40-month period. (3)
Amara is also accumulating capital for the initiative.
Amara starts with an initial allocation of £774 in the first month and, in each subsequent month, she reduces her allocation by £12 compared to the previous month, so that she allocates £762 in the second month, £750 in the third month, and so on, forming an arithmetic sequence.
Given that, after nnn months, Amara will have accumulated a total of exactly £21,600 for the fund,
form an equation in nnn and show that it can be simplified to
n2−130n+3600=0 n^2 - 130n + 3600 = 0 n2−130n+3600=0(3)
Solve the equation in part (c). (2)
State, with a reason, which of the solutions to the equation in part (c) is not a sensible value for nnn in this context. (1)
308 exam-style questions on OCR (MEI) A Level Maths 1.6 Sequences and Series, covering 1.6.1 Binomial expansion for positive integer n, 1.6.2 Factorial and combinations notation, 1.6.3 Binomial expansion for rational n (A-level only), 1.6.4 Binomial expansion of (a + bx)^n via factoring (A-level only), 1.6.5 Binomial approximating polynomials (A-level only), 1.6.6 What a sequence is; finite and infinite (A-level only), 1.6.7 Generate a sequence by formula or recurrence (A-level only), 1.6.8 A series as a sum of terms (A-level only), 1.6.9 Sigma notation (A-level only), 1.6.10 Increasing, decreasing and periodic sequences (A-level only), 1.6.11 Convergent and divergent sequences (A-level only), 1.6.12 Arithmetic sequences and series (A-level only), 1.6.13 Standard formulae for arithmetic series (A-level only), 1.6.14 Geometric sequences and series (A-level only), 1.6.15 Standard formulae for geometric series (A-level only), 1.6.16 Sum to infinity of a geometric series (A-level only), and 1.6.17 Sequences and series in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.