What number must be added to each of the numbers 1, 3, and 6 in order for the resulting numbers to form a geometric sequence?

Answer 1

let the number to be added be x

then :
(3+x)/(1+x) = (6+x)/(3+x)
(1+x)(6+x) = (3+x)(3+x)
6 + 7x + x^2 = 9 + 6x + x^2
x = 3

check:
the sequence would then be 4,6, and 9
which is a GP with r = 3/2

Answer 2

How we get 7x and 6x??