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Rajan@2021
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The 9th term of an AP is -32 and the sum of the 11th and 13th terms is -94. Find the common difference of the AP.

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An important and exam oriented question from arithmetic progression chapter in which we have been asked to find the common difference, if the 9th term of an AP is -32 and the sum of the 11th and 13th terms is -94.

RS Aggarwal, Class 10, chapter 5A, question no 30

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  1. Given: 9th term of an AP is -32 and the sum of its 11th and 13th terms is -94

    Now, a9 = a + 8d = -32 …(1)

    a11 = a + 10d

    a13 = a + 12d

    Sum of 11th and 13th terms: a11 + a13 = a + 10d + a + 12d

    -94 = 2a + 22d

    or a + 11d =-47 …(2)

    Subtracting (1) from (2) ,

    we have

    3d = -47 + 32 = -15

    or d = -5

    Common difference is -5.

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