Question

The sum of three numbers x, y, z which are in
G.P. is 56. Find x, y, z if x-1, y - 7 and z - 21
are in A.P.
​

Answer 1

Answer:

x = 8, y = 16, z = 32

or

x = 32, y = 16, z = 8

Step-by-step explanation:

we have,

x + y + z = 56 --------------- 1

x, y, z are in GP -> y * y = x * z

Also,

x - 1, y - 7 and z - 21 are three terms which are in Ap;

second term - first term = third term - second term

y - 7 - x + 1 = z - 21 - y + 7

2 * y - 7 - 7 + 1 + 21 = x + z

2 * y + 8 = 56 - y ( from equation 1 I took value of x + z)

y = 48 / 3 = 16.

x , y , z are in GP . And, we got the second value. Now, think of a series which will follow the GP series.

keep In mind -

x must be less than y and divides y completely.

z must be large than y and divisible by y completely.

y / x must be equal to z / y

Hence,

x = 8, y = 16, c = 32.

Thinking is very good skill we must think of answer at early steps of calculation rather than solving all the steps.

Note :- if you are a school student and not solving multiple choice question then solve further by yourself. Because you are having 2 unknowns and 2 equations to solve them.

As b = 16.

First equation -

x + z = 56-16 = 40

xz = 16*16 = 256