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Deepak Bora
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For what value of n, the nth terms of arithmetic progression 63, 65,67,…..and 3,10,17,….are equal?

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Question of RS Aggarwal book based on Arithmetic Progression For ICSE & CBSE Board Students.
Here the AP is given you have to find the value on which the n and the nth terms of AP are equal.
Question Number 21 Of Exercise 11A of RS Aggarwal Solution

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1 Answer

  1. In 1st AP:

    Given AP is 63,65,67…..

    First-term a = 63.

    Common difference d = 65 – 63 = 2.

    We know that sum of n terms an = a + (n – 1) * d

    = 63 + (n – 1) * 2

    = 63 + 2n – 2
    = 61 + 2n  ——- (1)

    In 2nd AP :

    Given AP is 3,10,17.

    First-term a = 3.

    Common difference d = 10 – 3 = 7.

    We know that sum of n terms an = a + (n-1) d

    = 3 + (n – 1) * 7

    = 3 + 7n – 7

    = 7n – 4  ——- (2)

    Given that nth term of these AP are equal.

    From (1) and (2),
    we get

    61 + 2n = 7n – 4

    61 + 4 = 7n – 2n

    61 + 4 = 5n

    65 = 5n

    n = 13.

    Therefore 13th term of these AP’s are equal

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