# EXERCISE 19.3

QUESTION 1

The sum of three terms of an A.P. is 21 and the product of the first and the third terms exceeds the
second term by 6, find three terms.

Sol :

Let the three terms of the A.P. be  ,  a ,

Then , we have

Also ,

When d = 6 , a = 7 ,putting in (a – d) , a , (a + d) we get :

1 , 7 , 13

When d = -6 , a = 7 ,putting in (a – d) , a , (a + d) we get :

13 , 7 ,1

QUESTION 2

Three numbers are in A.P. If the sum of these numbers be 27 and the product 648, find the
numbers.

Sol :

Let the three terms of the A.P. be  ,  a ,

Their sum = 27

Product

When d = 3 , a = 9 ,putting in (a – d) , a , (a + d) we get :

6 , 9 , 12

When d = -3 , a = 9 ,putting in (a – d) , a , (a + d) we get :

12 , 9 , 6

QUESTION 3

Find the four numbers in A.P., whose sum is 50 and in which the greatest number is 4 times the
least.

Sol :

Let the four numbers be , , ,

Their sum = 50

Also,

When , ,putting in , , ,

So , the terms are as follows :  , , ,

= 5 , 10 , 15 ,20

QUESTION 4

The sum of three numbers in A.P.is 12 and the sum of their cubes is Find the numbers.

Sol :

Let the three terms of the A.P. be ,  a ,

Their sum = 12

Also, sum of their cubes are

When d = 2 , a = 4 ,putting in (a – d) , a , (a + d) we get :

2 , 4 , 6

When d = -2 , a = 4 ,putting in (a – d) , a , (a + d) we get :

6 , 4 , 2

QUESTION 5

If the sum of three numbers in A.P. is 24 and their product is 440, find the numbers.

Sol :

Let the three numbers be

Their sum = 24

Also , their product is

When d = 3 , a = 8 ,putting in (a – d) , a , (a + d) we get :

5 , 8 , 11

When d = -3 , a = 8 ,putting in (a – d) , a , (a + d) we get :

11 , 8 , 5

QUESTION 6

The angles of a quadrilateral are in A.P. whose common difference is . Find the angles.

Sol :

Let the four angles be

Given : d = 10

Sum of all the angles is

,,, i.e.

ALTERNATE METHOD

Let the four angle be , , ,

Then ,

Sum of all the angle =

AND

The angle of the given quadrilateral are and