Two series X (x1, x2, x3, x4, ….xn) and Y (y1, y2, y3, y4, ….., yn

1.	Two series X (x1, x2, x3, x4, ….xn) and Y (y1, y2, y3, y4, ….., yn) are in A.P., such that xn – yn = n − 2. It is also known that x3= b5. Find the value of x99 – y197. (a) 47 (b) 48 (c) 49 (d) 50
Answer» Correct option (b) 48 Explanation: Let the common difference of the series X be d₁ and that of Y be d₂ Since x_n – y_n = n − 2, x₁ − y₁= −1 or y₁ = x₁+ 1 x₃ = y₅ x₁+ 2d₁ = y₁+ 4d₂ x₁ + 2d₁= x₁ + 1 + 4d₂ 2d₁ − 4d₂= 1 x₉₉– y₁₉₇= x₁+ 98d₁− y₁- 196d₂ = −1 + 49(2d₁− 4d₂) = −1 + 49 = 48.

Two series X (x1, x2, x3, x4, ….xn) and Y (y1, y2, y3, y4, ….., yn) are in A.P., such that xn – yn = n − 2. It is also known that x3= b5. Find the value of x99 – y197. (a) 47 (b) 48 (c) 49 (d) 50

Answer»

Correct option (b) 48

Explanation:

Let the common difference of the series X be d₁ and that of Y be d₂

Since x_n – y_n = n − 2, x₁ − y₁= −1 or y₁ = x₁+ 1

x₃ = y₅

x₁+ 2d₁ = y₁+ 4d₂

x₁ + 2d₁= x₁ + 1 + 4d₂

2d₁ − 4d₂= 1

x₉₉– y₁₉₇= x₁+ 98d₁− y₁- 196d₂ = −1 + 49(2d₁− 4d₂) = −1 + 49 = 48.

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Two series X (x1, x2, x3, x4, ….xn) and Y (y1, y2, y3, y4, ….., yn) are in A.P., such that xn – yn = n − 2. It is also known that x3= b5. Find the value of x99 – y197. (a) 47 (b) 48 (c) 49 (d) 50

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