Given that the coefficient of x³ in the expansion of (2 - 1/4x)ⁿ is 280, find the value of the positive integer n.

Mark scheme

Marking points from the official mark scheme. The mark or mark type is shown in brackets.

1. M1 for correctly identifying the term in x³ as binomn3 (2)ⁿ⁻³ (-1/4x)³
2. A1 for coefficient is binomn3 (2)ⁿ⁻³ (-1/4)³
3. M1 for setting up the equation binomn3 (2)ⁿ⁻³ (-1/4)³ = 280
4. M1 for expressing binomn3 as (n(n-1)(n-2))/(3 × 2 × 1) and attempting to simplify the powers of 2 and 4.
5. A1 for n=10 (showing sufficient working, e.g. (n(n-1)(n-2))/6 (2ⁿ)/(8 × 64) = 280 ⇒ n(n-1)(n-2) = 720 which leads to 10 × 9 × 8 = 720)