Question 1: Find three numbers in G.P. whose sum is and whose product is .

Answer:

Let the terms of the G.P. be

Given

Also given

or

Therefore when and , G.P. is

and when and , G.P. is

Question 2: Find three numbers in G.P. whose sum is and whose product is .

Answer:

Let the terms of the G.P. be

Given

Also given

or

Therefore when and , G.P. is

and when and , G.P. is

Question 3: The sum of the first three terms of a G.P. is and their product is . Find the G.P.

Answer:

Let the terms of the G.P. be

Given

Also given

or

Therefore when and , G.P. is

and when and , G.P. is

Question 4: The product of the first three terms of a G.P. is and the sum of their products taken in pairs is . Find them.

Answer:

Let the terms of the G.P. be

Given

Also

Therefore when and , G.P. is

and when and , G.P. is

Question 5: The sum of the first three terms of a G.P. is and their product is . Find the common ratio and the terms.

Answer:

Let the terms of the G.P. be

Given

Also given

or

Therefore when and , G.P. is

and when and , G.P. is

Question 6: The sum of three numbers in G.P. is . If the first two terms are each increase by and the third is decreased by , the resulting numbers are in A.P. Find the numbers.

Answer:

Let the terms of the G.P. be

Therefore

… … … … … i)

Also, new terms are in A.P.

Substituting from i) we get

Substituting the value of a in i) we get

Therefore when and , G.P. is

and when and , G.P. is

Question 7: The product of three numbers in G.P. is . If be added to them, the results are in A.P.. Find the numbers.

Answer:

Let the terms of the G.P. be

Therefore

Also, new terms are in A.P.

Substituting for a we get

Therefore when and , G.P. is

and when and , G.P. is

Question 8: Find three numbers in G.P. whose product is and the sum of their product in pairs is .

Answer:

Let the terms of the G.P. be

Therefore

Also

Therefore when and , G.P. is

and when and , G.P. is

Question 9: The sum of three numbers in G.P. is and the sum of their squares is . Find the numbers.

Answer:

Let the required numbers be

Therefore

… … … … … i)

Also

… … … … … ii)

Squaring both sides of i) we get

… … … … … iii)

Substituting this in i) we get

When and when

Therefore when and , G.P. is

and when and , G.P. is