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Question
Find x, y and z, given that the numbers x, 10, y, 24, z are in A.P.
Solution
A.P = x, 10, y, 24, z,…
d = t2 – t1 = 10 – x ...(1)
= t3 – t2 = y – 10 ...(2)
= t4 – t3 = 24 – y ...(3)
= t5 – t4 = z – 24 ...(4)
(2) and (3)
⇒ y – 10 = 24 – y
2y = 24 + 10 = 34
y = `34/2` = 17
(1) and (2)
⇒ 10 – x = y – 10
10 – x = 17 – 10 = 7
– x = 7 – 10
– x = – 3 ⇒ x = 3
From (3) and (4)
24 – y = z – 24
24 – 17 = z – 24
7 = z – 24
∴ z = 7 + 24 = 31
∴ Solutions x = 3
y = 17
z = 31
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