Question

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

Answer 1

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