Find x, y and z, given that the numbers x, 10, y, 24, z are in A.P.

Solution :

Since the given sequence is an arithmetic progression,

t2 - t1 = 10 - x ---(1)

t3 - t2 = y - 10 ---(2)

t4 - t3 = 24 - y ---(3)

t5 - t4 = z - 24 ---(4)

By applying the value of y in x + y = 20

x + 17 = 20

x = 3

(3) = (4)

24 - y = z - 24

y + z = 24 + 24

y + z = 48

17 + z = 48

z = 31

Hence the values of x, y and z are 3, 17, 31 respectively.