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Sum of first six terms of an AP is 42. The ratio of its 10th term to 30th term is 1:3 find the first and 13th term of an AP.

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We have been given that the sum of first six terms of an AP is 42. The ratio of its 10th term to 30th term is 1:3 find the first and 13th term of an AP.

ML Aggarwal

Avichal Publication

Arithmetic Progression

Chapter 9 Question no 15

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1 Answer

  1. Sum of the first n terms is given by

    Sn=2n[2a+(n1)d]

    S6=26[2a+(61)d]

    S6=3[2a+5d]

    T30T10=31

    a+29da+9d=31

    (a+9d)3=(a+29d)1

    3a+27d=a+29d

    2a=2d

    a=d…(1)

    S6=3[2a+5d]

    S6=3[2a+5a]

    42=3(7a)

    42=21a

    a=2

    From (1)

    d=a=2

    T13=a+(n1)d

    =2+(131)2

    =2+24

    =26

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