What are x and y if 5 x y 40 are in a Geometric Progression?

Answer 1

For Geometric Progression

#1 = a = 5

#2 = ar = x

#3 = ar^2 = y

#4 = ar^3 = 40

We need to find 'r'

To do this ,divide #4 by #1 , hence

ar^3 / a = 40 / 5

Hence r^3 = 8 (Notice the 'a' cancels down to leave 'r^3'

Cube root both sides

Hence r = 2

When r = 2

#2 = ar = 5 X 2 = 10 = x

#3 = ar%2 - 5 x 2^2 = 5 x 4 = 20 = y

So the geometric progression is 5,x,y,40 = 5,10,20,40

Answer 2

In a GP each term is the previous term multiplied by a constant.

Let the common difference be r, then:

x = 5r

y = xr = 5rr = 5r²

40 = yr = 5r²r = 5r³

→ 5r³ = 40

→ r³ = 8

→ r = 2

→ x = 5 × 2 = 10

→ y = 10 × 2 = 20