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.*

**Teacher notes:**

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.

**Solutions:**

You can download the solution pdf here.

Can you *prove* your hypothesis?