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

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)

(1)  = (2) 10 - x  = y - 10 x + y  = 20

(2) = (3) y - 10  = 24 - y y + y  = 24 + 10 2y  = 34 y  = 17

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.