Consecutive integers are arranged in rows. Each highlighted shape selects a and b one row above its centre n, and c and d one row below, one column to either side.

(a(i)) For the 5-column grid and n = 13, find bc − ad. [1]

(a(ii)) Given a = n − 6, express b, c and d in terms of n. [2]

(a(iii)) Show algebraically that bc − ad = 20. [2]

(b(i)) For the 6-column grid and n = 10, find bc − ad. [1]

(b(ii)) Write bc − ad in terms of n without simplifying. [2]

(c) For the 7-column grid, show bc − ad = 28 when n = 17. [1]

(d) Write bc − ad for a grid with t columns. [1]

(e) For the last shape, find c, d and bc − ad. [2]