Q3 of 202 Page 9

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

Let the four numbers be (a – 3d), (a – d), (a + d) and (a + 3d)

a – 3d + a – d + a + d + a + 3d = 50


4a = 50


a =


According to question,


(a + 3d) = 4(a – 3d)


a + 3d = 4a – 12d


3a = 15d


5d =


d =


Therefore,


a – 3d = - = 5


a – d = - = 10


a + d = + = 15


a + 3d = + = 20


More from this chapter

All 202 →
1

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

 2

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

 4

The angles of a quadrilateral are in A.P. whose common difference is 10°. Find the angles.

 5

The sum of three numbers in A.P. is 12 and the sum of their cube is 288. Find the numbers.