# EXERCISE 20.2

QUESTION 1

Find three numbers in G.P. whose sum is 65 and whose product is 3375 .

Sol :

Let the terms of the the given G.P. be , a and

Then, product of the G.P. =3375

a = 15

Similarly, sum of the G.P.

Substituting the value of a

Hence, the G.P.for a=15 and is 45 , 15 , 5

And, the G.P. for a=15 and r=3 is 5 , 15 , 45

QUESTION 2

Find three numbers in G.P. whose sum is 38 and their product is 1728

Sol :

Let the terms of the the given G.P.be , a and

Then, product of the G.P. = 1728

a = 12

Similarly, sum of the G.P. = 38

Substituting the value of a

Hence, the G.P. for and is and

And, the G.P. for and is and 18

Hence, the three numbers are 8 , 12 and 18

QUESTION 3

The sum of first three terms of a G.P.is and their product is -1 Find the G.P.

Sol :

Let the first three numbers of the given G.P. be , a and ar

Product of the G.P. = -1

a = -1

Similarly, Sum of the G.P.

Substituting the value of a=-1

Hence, the G.P. for and is and

And, the G.P. for and is and

QUESTION 4

The product of three numbers in G.P. is 125 and the sum of their products taken in pairs is Find them.

Sol :

Let the required numbers be , a and ar

Product of the G.P. = 125

a = 5

Sum of the products in pairs

Substituting the value of a

Hence, the G.P. for and is and

And, the G.P. for and is and

QUESTION 5

The sum of first three terms of a G.P. is and their product is 1  . Find the common ratio and the terms.

Sol :

Let the terms of the G.P be , a and ar.

Product of the G.P. = 1

a = 1

Now, sum of the G.P.

Hence, putting the values of and the required numbers are or and

QUESTION 6

The sum of three numbers in G.P. is 14  . If the first two terms are each increased by 1 and the third term decreased by 1 , the resulting numbers are in A.P. Find the numbers.

Sol :

Let the numbers be a, ar and

Sum = 14

According to the question, , and are in A.P.

[from (i)]

Putting in (i)

Putting in (ii), we get

So, the G.P. is and 2

Similarly putting in (ii), we get .

So, the G.P is and 8

QUESTION 7

The product of three numbers in G.P. is 216 . If be added to them, the results are in A.P. Find the numbers.

Sol :

Let the terms of the given G.P. be , a and ar.

Product = 216

a = 6

It is given that and are in A.P.

Putting we get

Hence, putting the values of and the required numbers are or and 18

QUESTION 8

Find three numbers in G.P. whose product is 729 and the sum of their products in pairs is 819

Sol :

Let the required numbers be , a and ar.

Product of the G.P.

a = 9

Sum of the products in pairs

Hence, putting the values of and we get the numbers to be and 1 or and 81

QUESTION 9

The sum of three numbers in G.P. is 21 and the sum of their squares is 189  Find the numbers.

Sol :

Let the required numbers be ar and

Sum of the numbers

Sum of the squares of the numbers

ii

Now, [from(i)]

Squaring both the sides

[using (ii)]

[using (i)]

Putting in

Putting in we get

So, the numbers are and 3

Putting in we get

So, the numbers are and

Hence, the numbers that are in G.P are and