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

1.	Find x, y and z, given that the numbers x, 10, y, 24, z are in A.P.
Answer» 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 = 43/2 = 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

Answer»

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 = 43/2 = 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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