Question

Given the sequence:4;x;32.Determine the value(s) of x if the sequence is:

1.arithmetic
2.geometric

Answer 1

AP:
x-4 = 32-x
2x=36
x=18
AP=4,18,32

GP:
x/4 = 32/x
x^2 = 128
x = ±√128
GP=4,√128,32
or
4,-√128,32

Answer 2

Arithmetic Progression - applying common difference,

$x-4=32-x$

$2x=32+4$

$2x=36$

$x= 18$

Geometric Progression - apply common ratio,

$\dfrac{x}{4} = \dfrac{32}{x}$

$x^2 =128$

$x = \pm \sqrt{128}$