Question

in an AP the 2nd and 5th term are respectively (x-y)(x+y) then the thrice the first term is ​

Answer 1

Step-by-step explanation:

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Answer 2

Given:

In an Arithmetic Progression, the 2nd term is x-y, and the 5th term is x+y.

To Find:

The thrice of the first term is?

Solution:

The given problem can be solved using the concepts of Arithmetic progressions.

1. The second term and fifth terms are x-y and x+y respectively.

2. In an A.P the nth term is given by a general formula,

=>$T_{n} = a+(n-1)d$,

3. Using the above formula,

• The second term can be written as a + d = x - y,(Consider as equation1)
• The fifth term can be written as a + 4d = x + y,(Consider as equation2)

4. Solve equations 1 and 2 for values of a and d,

=> Subtract equation 2 from equation 1,

=> a + d - a - 4d = x - y - (x + y),

=> -3d = -2y,

=> d = (2y/3).

5. Substitute the value of d in equation 1.

=> a + 2y/3 = x - y,

=> a = x - y - 2y/3,

=> a = x - (5y/3).

6. The first term in the A.P is x - (5y)/3.

=> Thrice of the first term is 3(x - (5y)/3),

=> Thrice of the first term = 3x - 5y.

Therefore, the thrice of the first term is 3x - 5y. Option D is the correct answer.