# Arithmetic Progression: Find x and y

If 3, x, y and18 are arithmetic progression (A.P), find x and y.[email_link]

http://solvemaths.in/arithmetic-progression-find-x-and-y/AptitudeArithmeticContestIf 3, x, y and18 are arithmetic progression (A.P), find x and y.

Rajni
Sahsah.rajni@yahoo.comAdministratorSOLVE - ΜΔΓΗŠ
3, x, y and 18 are an arithmetic progression

The difference between any two consecutive numbers in AP is the same.

Any nth number in an AP series is given as

A(n) = A(1) + (n-1)*d, where d is the common difference between consecutive numbers and A(1) is the first term in the series.

In our example, A(1) = 3

d = (x-3) = (18-y)

x-3 = 18 -y => x+y = 21 ——- (i)

Given, Fourth number in series A(4) = 18

By formula, A(4) = A(1) + 3d

or, 18 = 3 + 3d

or, 18 = 3 + 3(x-3)

or, 15 = 3x – 9

or, x = 8 ———— (ii)

Substitute eq (ii) in eq (i)

x+y = 21

or, 8+y = 21

or, y = 13 ———— (iii)