Question

What number should be added to each of the three numbers 1, 7, and 19 so that the resulting three numbers form a geometric progression?

Answer 1

The answer is 5 but i'm not sure how to get there.

Answer 2

If the resulting numbers (a1, a2 and a3) form a geometric progression they must fulfill:
a2=a1·r--->a2/a1=r
a3=a2·r--->a3/a2=r

We can say: a2/a1=a3/a2 <--->a2·a2=a1·a3 (1)
But we know that
a1=1+x
a2=7+x
a3=19+x
Then we can replace in (1)
(7+x)(7+x)=(1+x)(19+x)---> 49+14x+x^2=19+20x+x^2--->49+14x=19+20x--->
49-19=30=20x-14x=6x--->6x=30--->x=5

Answer 3

easy, isnt it?

Answer 4

Much easier when we simplify it to a1 a2 and a3 before approaching it! Thank you so much!

Answer 5

you are welcome