Answer:
X=10, Y=20,Z=80
Step-by-step explanation:
We are given that the numbers X,Y and Z are in the ratio 1:2:8
Let the numbers be:
X=x
Y=2x
Z=8x
Now we are given that 40 is subtracted from Z such that the numbers X,Y,Z-40 form a geometric sequence.
that means x,2x,8x-40 forms a geometric sequence.
Also if a,b,c are in geometric progression then they have same common ratio.
i.e. [tex]\dfrac{b}{a}=\dfrac{c}{b}[/tex]
[tex]\dfrac{2x}{x}=\dfrac{8x-40}{2x}[/tex]
[tex]\dfrac{2}{1}=\dfrac{8x-40}{2x}\\ \\4x=8x-40\\\\8x-4x=40\\\\4x=40\\\\x=10[/tex]
Hence, the number X =10
Y=2×10=20
Z=8×10=80
The numbers X, Y and Z of the given geometric sequence are; 10, 20, 80
We are given the numbers X,Y and Z are in the ratio 1:2:8
Thus, the numbers are;
X = x
Y = 2x
Z = 8x
We are told that 40 is subtracted from Z such that the numbers X,Y,Z - 40 form a geometric sequence.
This means that the sequence is now;
x, 2x, 8x - 40
In geometric sequence, consecutive numbers have same common ratio. Thus; Y/X = (Z - 40)/Y
⇒ 2x/x = (8x - 40)/2x
⇒ 2 = (8x - 40)/2x
Cross multiply to get;
4x = 8x - 40
8x - 4x = 40
4x = 40
x = 10
Thus;
Y = 2 * 10 = 20
Z = 8 * 10 = 80
Read more about Geometric Sequence at; https://brainly.com/question/24643676
