# Maths

If 192;x;y;3 form a geometric progression, calculate the value of x and y.

1. 👍 0
2. 👎 0
3. 👁 145
1. 3d = 3-192 = -189
d = -63

192;129;66;3

1. 👍 0
2. 👎 0
2. 192,x,y,3,.....
t1 ,t2,t3,t4,...
if it is in GP then
(t2/t1)=(t3/t2)=(t4/t3)
then (t2/t1)=x/192.........(1)
(t3/t2)=y/x...........(2)
(t4/t3)=3/y...........(3)
Now (1)=(2)

x/192=y/x
=>192y=x^2.......(4)

Also
(2)=(3)

y/x=3/y

=>3x=y^2.........(5)

from (2)=> (y^2)/3 substitute in (4)

=>192y=((y^2)/3)^2
=>192y=(y^4)/9
=>192*9=y^3
=>1728=y^3

=>y=12 substitute in (5)

=>we get x=48

therfore x=48,y=12
then verify the series
192,48,12,3........

Hence solved.

1. 👍 0
2. 👎 0

## Similar Questions

1. ### math

1)Find the sum of the first eight terms of the Geometric progression 256,128,64,32 2)How many terms should be taken from the Geometric progression 4,12,36 for the sum to be 2188

asked by la bellgoss on March 19, 2011
2. ### algebra

The sum of the three numbers in Arithmetic Progression is 33. If the numbers are increased by 2, 1, and 6 respectively the new numbers will be in Geometric progression. Find these numbers.

asked by jude on April 10, 2017
3. ### math

Three numbers form a geometric progression. If the second term is increased by 2, then the progression will become arithmetic and if, after this, the last term is increased by 9, then the progression will again become geometric.

asked by Anonymous on January 28, 2017
4. ### math

k+1,2k-1,3k+1 are three consecutive terms of a geometric progression, find the possible values of the common ratio

asked by charity on October 20, 2015
5. ### Math

Three numbers form a geometric progression. If 4 is subtracted from the third term, then the three numbers will form an arithmetic progression. If, after this, 1 is subtracted from the second and third terms of the progression,

asked by Anonymous on December 30, 2015
1. ### math

The first, the third and the seventh terms of an increasing arithmetic progression are three consecutive terms of a geometric progression. In the first term of the arithmetic progression is 10 find the common difference of the

asked by kudu on February 2, 2015
2. ### Algebra 2

In an infinite geometric progression with positive terms and with a common ratio |r|

asked by Alex Chien on February 4, 2017
3. ### math

The third,sixth and seventh terms of a geometric progression(whose common ratio is neither 0 nor 1) are in arithmetic progression. Prove dat d sum of d first three is equal to d fourth term

asked by toyinbo on March 6, 2015
4. ### Maths

A Geometric progression X has a first term of 4a and its sixth term is 256. Another Geometric progression Y has a first term of 3a and its fifth term is 48. Find the: (i) First term of X (ii) Sum of the first four terms of X

asked by Ande2 on June 24, 2019
5. ### Math

The common ratio of a geometric progression is 1/2 , the fifth term is 1/80 , and the sum of all of its terms is 127/320 . Find the number of terms in the progression.

asked by Alisha on January 27, 2020
6. ### math

There are two positive numbers that can be inserted between 3 and 9 such that the first three are in geometric progression while the last three are in arithmetic progression. Find the sum of those two numbers.

asked by Sidney on February 14, 2011