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The sum of the first four terms of an A....

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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The correct Answer is:
11 terms
Let the A.P. be 11,11+d,11+2d,11+3d,…,11+(n-2)d,11+(n-1)d.
Sum of first four terms=11+(11+d)+(11+2d)+(11+3d)
=44+6d
Sum of last four terms=[11+(n-4)d]+[11+(n-3)d]+[11+(n-2)d]+[11+(n-1)d]
=44+(4n-10)d
According to the given condition,
44+6d=56`rArr`d=2
and 44+(4n-10)d=112
or 44+2(4n-10)=112
or n=11
Thus, the number of terms of the A.P is 11
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