In the following grids, each blank square should be filled with the mean of the two numbers in adjacent squares.
(a) Fill in the grid below.
(b) Find x in the following grid, leaving your answer in terms of a,c:
(c) Find x in the following grid, leaving your answer in terms of a,c:
(d) For a grid of length n with first box a and last box c, make a hypothesis for the value of x, the box adjacent to c in terms of a,c,n.
(e) Check your hypothesis works when a = 10, b = 15, n = 6.
Level of difficulty: Accessible for good SL and HL students
Syllabus knowledge required: Basic averages and algebraic manipulation
This could be done when doing mean, median mode.
You can download the solution pdf here.
Can you prove your hypothesis?