Q29 of 52 Page 1

If the sum of the first 7 terms of an A.P. is 119 and that of the first 17 terms is 714, find the sum of its first n terms.

Given,


Sum of first 7 terms of an AP = 119


Sum of first 17 terms of an AP = 714


Sn = n/2(2a+(n – 1)d]


Case 1,


S7 = 119


7/2[2a+(7 – 1)d] = 119


7/2×2(a+3d) = 119


a+3d = 119/7 = 17


a = 17 – 3d …..(i)


Case 2,


S17 = 714


7/2[2a+(7 – 1)d] = 714


a+8d = 714/17 = 42


By putting (i),


17 – 3d + 8d = 42


So, here we have;


5d = 42 – 17 = 25


d = 25/5 = 5


From Eq.(i) and (ii),


a = 17 – 3 (5) = 17 – 15 = 2


sn = n/2 [2a(n – 1)d]


sn = n/2 [2(2)+(n – 1) 5]


= n/2 [4+5n – 5]


= n/2[5n – 1]


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