Q. 315.0( 1 Vote )

The sum of the fi

Answer :

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 question -


4a + 6d = 66


4(11) + 6d = 66 [ a = 11 (given)]


6d = 12


d = 2


and,


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 the A.P. is 11.

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