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86. The sum of the first four terms of an A.P. is 56. The sum of the last four terms is 112. If its first term is 11, then find the number of terms.

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    Answered by

    Payal Gupta | Contributor-Level 10

    4 months ago

    86. Given, a = 11

    Let d and l be the common difference & last term of the A.P.

    Then, a+(a+d)+(a+2d)+(a+3d)=56 [first 4 terms sum]

    ⇒4a+6d=56

    ⇒6d=56−4a=56−4×11=56−44=12

    ⇒d=126=2

    And, l+(l−d)+(l−2d)+(l−3d)=112

    ⇒4l−6d=112

    ⇒4l=112+6d=112+6×2=112+12=124 [last 4 terms sum]

    ⇒l=1244=31

    So, l=31

    ⇒a+(n−1)d=31

    ⇒11+(n−1)2=31

    ⇒(n−1)2=31−11=20

    ⇒n−1=202=10

    ⇒n=10+1

    ⇒n=11

    the A.P. has 11 number of terms.

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