Question

the sum of four number in AP is 50 and the greatest number four times the least find the numbers​

Answer 1

SOLUTION

Let the AP be a, a+d, a+2d, a+3d.

sum of AP = 50

therefore,

=) a+a+d+a+2d+a+3d= 50

=)4a+6d= 50

=)2a+ 3d= 25...........(1)

also given,

The greatest Number is 4 times the least

=) 4(a)= a+3d

=) 4a= a+ 3d

=) 4a-a= 3d

=) 3a= 3d

=) a= d

Putting a= d in (1) , we get

=) 5d= 25

=) d= 25/5

=) d= 5

a= 5 as d= 5

first, four terms are

=) 5, 10, 15, 20

HOPE it helps ✔️

Answer 2

5,10,15,20

Step-by-step explanation:

Let the four numbers in the A.P are a,2a,3a,4a

according to question

$a+2a+3a+4a=50\\10a=50\\a=5$

$\therefore$the number in the A.P are 5,10,15,20