The sum of first 4 terms of an A.P. is 56 and the sum of last 4 terms is 112. If its first term is 11, find the number of terms.

Question

The sum of first 4 terms of an A.P. is 56 and
the sum of last 4 terms is 112. If its first term
is 11, find the number of terms.
[NCERT)​

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Kaylee 3 days 2021-09-09T16:27:32+00:00 1 Answer 0 views 0

Answers ( )

    0
    2021-09-09T16:28:42+00:00

    Answer:

    Here is your answer

    Step-by-step explanation:

    Let the A.P. be a,a+d,a+2d,a+3d,…a+(n−2)d,a+(n−1)d.

    Sum of  first four terms =a+(a+d)+(a+2d)+(a+3d)=4a+6d

    Sum of last four terms

    =[a+(n−4)d]+[a+(n−3)d]+[a+(n−2)d]+[a+(n−1)d]⇒=4a+(4n−10)d

    According to the given condition, 4a+6d=56

    ⇒4(11)+6d=56

    Since

    a=11(given)]⇒6d=12⇒d=2∴4a+(4n−10)d=112⇒4(11)+(4n−10)2=112⇒(4n−10)2=68⇒4n−10=34⇒4n=44⇒n=11

    Thus the number of terms of A.P. is 11.

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