Edexcel IALGeneralGeneral Applications8 Marks
(i) Find the exact value of `\sum_{r=1}^{10} (r^3 + 1)`. (ii) A sequence `u_1, u_2, u_3, ...` is defined by `u_n = 4n-1`. Find the value of `k` such that `\sum_{r=1}^{k} u_r = 728`.
- (i)Find the exact value of `\sum_{r=1}^{10} (r^3 + 1)`.[4]
- (ii)A sequence `u_1, u_2, u_3, ...` is defined by `u_n = 4n-1`. Find the value of `k` such that `\sum_{r=1}^{k} u_r = 728`.[4]
Mark scheme
Marking points from the official mark scheme. The mark or mark type is shown in brackets.
- M1 for `\sum r^3 + \sum 1` (or `(n(n+1)/2)^2 + n`).
- A1 for using `n=10` in `(n(n+1)/2)^2 + n` or `(10(11)/2)^2 + 10`.
- A1 for `55^2 + 10` or `3025 + 10`.
- A1 for `3035`.
- B1 for `u_1 = 3` (or `a=3`) and `d=4`.
- M1 for using correct formula for sum of AP with `n=k` (or `n` for `k`). e.g. `S_k = k/2(2(3) + (k-1)4) = 728` or `k/2(3 + (4k-1)) = 728`.
- A1 for simplifying to a 3 term quadratic e.g. `2k^2 + k - 728 = 0`.
- A1 for `k=19`. (Reject `k=-19.5`).
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