# 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