arithmetic sequences meets equations

this task was devised by Martin Wilson, of Harrogate
the powerpoint is here

students could substitute numbers (trial and improvement)

or, if they appreciate that there are equal 'steps' between adjacent (and other) pairs of terms,
they can set up and solve linear equations with the unknown on both sides

for the quadratic version there may appear to be two solutions
but checking will show that, actually, only one of these works