Question

The sum of first 8 of an ap is 100 and sum of first 19 terms is 551 find ap

Answer 1

here S8=100, S19=551
to find the AP

Sn = n/2 [2a + (n-1) × d]
S8= 8/2 [2a + (8-1) × d]
100= 4 [2a + 7d]
100/4=2a + 7d
2a + 7d = 25------------(1)

S19= 19/2 [2a +(19-1) × d ]
551 =9.5 [2a + 18d]
551/9.5=2a + 18d
2a + 18d= 58-----------(2)

subtracting eq^n no.1 from eq^n no.2
_ 2a + 18d= 58
2a + 7d = 25
---------------------
11d = 33
d = 33/11
d = 3

put d=3 in eq^n no.1
2a + 7d = 25
2a + 7×3=25
2a + 21 =25
2a =25-21
2a =24
a = 24/2
a = 12

t1 = a = 12
t2= a+d= 12+3 =15
t3=t2+d =15+3=18
t4=t3+d =18+3=21

therefore required AP is
t1 , t2 , t3 , t4.......................
12 , 15 , 18 , 21 ....................