Question

Tge sum of first 8 is 100 and sum of its first 19 terms is 551 find ap

Answer 1

S8= 100, S19= 551
Sn= n/2(2a+(n-1)d)
S8= 8/2(2a+(8-1)d)
S8= 4(2a+7d)
100= 8a+28d...........................(1)

S19= 19/2(2a+18d)
551= 19a+ 171d ....................(2)
From (1) & (2)
152a+532d= 1900......................(3)
152 a+ 1368d= 4408..................(4)

Using elimination method ie solving eq (3) and (4)
ie 152 a + 532d = 1900
152 a +1368d = 4408
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-836 d = - 2508
d= 3
Therefore a= 2