Question

the sum of the first 8 terms of an ap is 100 and the sum of its first 19 terms is551. Find the first and the common difference?

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 ------------------------------------------- -836 d = - 2508 d= 3 Therefore a= 2

Answer 2

Refer the attachment:

hope helped:)