Question

What is 15th term of an ,
A Pis x+y,x-y ,x-3y

Answer 1

Hey friend,

Here is your answer,
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A.P.  -  x+y , x-y , x-3y ........

First term(a) = x+y

Common difference(d) = (x-y) - (x+y)
                                     = x-y-x-y
                                     = -2y

Number of terms(n) = 15


Tn = a+(n-1)d

T₁₅ = (x+y) + (15-1)*(-2y)

=> T₁₅ = x+y + 14*(-2y)

=> T₁₅ = x + y - 28y

      _____________
=> ║ T₁₅ = x - 27y ║
      ---------------------

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Hope this helped you !!
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Answer 2

Answer:

The 15th term of that AP is x -27y.

Step-by-step explanation:

Given that,

AP is x +y , x-y , x-3y........................

To find,

15th term of that AP ......?

Explanation,  

According the Question,

let's assume,

    a = 1st term of an AP.

    b = 2nt term of an AP. and,

    d = Common difference of an AP

So, we have

1st term of an AP, a = x+y,

2nt term of AP, b = x-y,

Common difference of an AP, d = 2nt term of an AP - 1st term of an AP

                                            = b-a

                                            = (x-y) - (x+y)

                                            = x -y - x -y

                                         d = -2y

We know that

      $T^{th}$ term of an AP = a + (n -1)d

Where, n is the number of term.

So, we can say that

      15th term of an AP = a + (15-1)d

Now, putting the all values,

So, we get

                                    =  (x-y) + 14 × (-2y)

                                    =  (x-y) - 28y

                                    = x -y - 28y

                                    = x -27y

Answer :- The 15th term of that AP is x -27y.

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