Question

If four numbers in A.P. are such that their sum is 50 and the greatest number is 4 times, the least, then the numbers are

Options

• 5, 10, 15, 20

• 4, 101, 16, 22

• 3, 7, 11, 15

•  none of these

Answer 1

Here, we are given that four numbers are in A.P., such that their sum is 50 and the greatest number is 4 times the smallest.

So, let us take the four terms as a - d , a , a + d , a + 2d.

Now, we are given that sum of these numbers is 50, so we get,

( a - d ) + (a) + ( a+ d ) + ( a + 2d) = 50

             a - d + a + a + d + a + 2d = 50

                                          4a + 2d = 50

                                            2a + d = 25                  ............(1) 

Also, the greatest number is 4 times the smallest, so we get,

a +2d = 4 ( a - d) 

a + 2d = 4a - 4d 

4d + 2d = 4a - a

        6 d = 3a

          `d = 3/6 a `                      ....................(2) 

Now, using (2) in (1), we get,

`2a + 3/6 a = 25` 

`(12a + 3a)/6 = 25 `

             15a = 150

              ` a = 150/15`

               a = 10 

Now, using the value of a in (2), we get,

`d = 3/6 (10)`

` d = 10/2` 

  d = 5 

So, first term is given by,

a - d = 10 - 5 

         = 5

Second term is given by,

a = 10 

Third term is given by,

 a + d = 10 + 5 

           = 15 

Fourth term is given by,

a + 2d = 10 + (2) (5)

            = 10 + 10 

             = 20

Therefore, the four terms are  5, 10 , 15, 20.