Question

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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Answer 1

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[Sincea=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.