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.

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