The sum of first 8 terms of an AP is 100 and sum of first 19 terms is 551. Find the AP
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
Verified answer
Let a be first term and d be common differenceA/q
(8/2)[2a+(8-1)d] = 100
⇒2a + 7d =25_____(1)
and (19/2)[2a + (19-1)d] = 551
⇒2a + 18d = 58____(2)
subtracting equation (1) and (2)
11d = 33
⇒d = 3
so a = (25 - 21)/2 = 2
so AP = 2,5,8.11,14.......
And:
S8 = 100
S19= 551
Sn = n/2{2a+(n-1)d}
S8=8/2{2a+(8-1)d}
100=4{2a+7d}
2a+7d=25
S19= 19/2 {2a+(19-1)d}
551×2/19=2a+18d
2a+18d=58
By Elimination Method
2a+18d=58
(-) 2a+ 7d=25
------------------------
11d=33
d=3
2a+7d= 25
2a+7(3)=25
2a=25-21
a=4/2
a = 2
AP = 2,5,8,11,14....…...