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If the Xth term of an A.P is 1/Y and the Yth term of an A.P is 1/X, what is the 2XYth term?
  • a)
    1
  • b)
    1/2
  • c)
    2
  • d)
    None of these
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
If the Xth term of an A.P is 1/Y and the Yth term of an A.P is 1/X, w...
To find the 2XYth term of an arithmetic progression (A.P.), we first need to determine the common difference between consecutive terms.

Let's assume the common difference is 'd'.

Given that the Xth term of the A.P. is 1/Y, we can write the formula for the Xth term as:

a + (X - 1)d = 1/Y

Similarly, the Yth term of the A.P. is 1/X, so we can write the formula for the Yth term as:

a + (Y - 1)d = 1/X

Now we have two equations and two variables (a and d) that we need to solve.

Solving the equations:

a + (X - 1)d = 1/Y ...........(1)
a + (Y - 1)d = 1/X ...........(2)

Subtracting equation (2) from equation (1), we get:

(X - 1)d - (Y - 1)d = 1/Y - 1/X
d(X - Y) = (X - Y)/(XY)
d = 1/(XY)

Now that we have the value of 'd', we can find the 2XYth term of the A.P. by substituting the values of 'a', 'd', and 'n' into the formula for the nth term of an A.P.:

T(n) = a + (n - 1)d

Substituting n = 2XY, a = 1/Y, and d = 1/(XY) into the formula:

T(2XY) = 1/Y + (2XY - 1)(1/(XY))
= 1/Y + (2XY - 1)/(XY)
= (1 + 2XY - 1)/(XY)
= 2XY/(XY)
= 2

Therefore, the 2XYth term of the A.P. is 2.

Hence, the correct answer is option C) 2.
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Community Answer
If the Xth term of an A.P is 1/Y and the Yth term of an A.P is 1/X, w...
A + (X - 1)D = 1/Y and A + (Y - 1)D = 1/X
So A = D = 1/XY
So the 2XYth term is 1/XY+(2XY-1)/XY = 2
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Given sequence: 3, 11, 34, 69, 131, 223To find the pattern in the sequence, let's calculate the differences between consecutive terms:11 - 3 = 834 - 11 = 2369 - 34 = 35131 - 69 = 62223 - 131 = 92The differences between consecutive terms are not following a consistent pattern. Therefore, the given sequence does not have a simple arithmetic or geometric progression.However, if we observe the differences between the differences, we can see a pattern:23 - 8 = 1535 - 23 = 1262 - 35 = 2792 - 62 = 30The differences between the differences are increasing by a constant value. This indicates that the given sequence might have a polynomial pattern.To find the polynomial pattern, we can use the method of finite differences. Let's calculate the second differences:15 - 12 = 312 - 27 = -1527 - 30 = -3The second differences are not constant. Therefore, the given sequence might have a polynomial of degree 2.Let's assume the polynomial is of the form ax^2 + bx + c. Substituting the given terms into the polynomial, we can form the following equations:1. 3a + b + c = 32. 9a + 3b + c = 113. 16a + 4b + c = 34Solving these equations, we get a = 1, b = 2, and c = 0.Therefore, the polynomial pattern for the given sequence is x^2 + 2x.Now, let's find the missing terms in the sequence

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If the Xth term of an A.P is 1/Y and the Yth term of an A.P is 1/X, what is the 2XYth term?a)1b)1/2c)2d)None of theseCorrect answer is option 'C'. Can you explain this answer?
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