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Deepak Bora
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How many terms of the Arithmetic Progression 45, 39, 33, … must be taken so that their sum is 180 ? Explain the double answer.

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CBSE 10th Class past year question paper

Year 2019

SET 1, Code Number- 30/2/1

Question number – 29 (b)

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1 Answer

  1. Sn = n/2 × { 2a + ( n – 1 ) d }

    180 = n/2 × [90 (n – 1)(–6)]

    360 = 90n – 6n² + 6n

    6n² – 96n + 360 = 0

    6 ( n² – 16 + 60 ) = 0

    n² – 16 + 60 = 0

    n² – 10n – 6n + 60 = 0

    n ( n – 10 ) – 6 (n – 10 ) = 0

    ( n – 6 ) ( n – 10 ) = 0

    n = 6, n = 10

    ∴ n = 6 or n = 10

     

     

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