Answer:
5 , 4.5, 13.5 and 40.5
Explanation:
Since the numbers are in geometric progression, their form is essentially:
a, ar, ar^2 and ar^3
Where a and r are first term and common ratio respectively.
From the information given in the catalog:
Third term is greater than the first by 12 while fourth is greater than second by 36.
Let’s now translate this to mathematics.
ar^2 - a = 12
ar^3 - ar = 36
From 1, a(r^2 - 1) = 12 and 2:
ar(r^2 - 1) = 36
From 2 again r[a(r^2 -1] = 36
The expression inside square bracket looks exactly like equation 1 and equals 12.
Hence, 12r = 36 and r = 3
Substituting this in equation 1,
a( 9 - 1) = 12
8a = 12
a = 12/8 = 1.5
Thus, the numbers are 1.5, (1.5 * 3) , (1.5 * 9), (1.5 * 27) = 1.5 , 4.5, 13.5 and 40.5