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)