Question

The sum of first 8 terms of an ap is hundred and sum of first 19 term is 551 find AP .

Answer 1

Answer:

Step-by-step explanation:

Sn = n/2(2a + (n–1)d)

For n= 8

We know S8 = 100

100 = 8/2(2a+(8–1)d)

100 = 4(2a+7d)

2a+7d = 25......(1)

For n = 19

We know S19 = 551

551 = 19/2(2a+(19–1)d)

551*2/19 = 2a+18d

29*2 = 2a+18d

a+9d = 29.........(2)

Equating 1 and 2

2a+7d = 25

a+9d = 29

Multiplying 2nd equation by 2

–(2a+7d = 25)

2(a+9d = 29

–2a–7d = –25

2A+18d = 58

11d = 33

d = 3

Substituting d in equation 2

a+9(3) = 29

a = 29–27

a = 2

AP

2,5,8,11,14,17.......

Hope this helps you

Answer 2

Answer:

Sn=n/2 {2a+(n-1)d}

Sn =8/2 (2a+(8-1)d)

100=4 (2a+7d)

100=8a+28d

100-28d/8=a..........1

Sn19=551

Sn=n/2 {2a+(n-1)d}

sn =19/2 {2a+(19-1)d}

551=19/2 {2×(100-28d/8)+18d}....from equation (1)

1102=19 (100-28d+72d)/4

1102=19 (100+44d)/4

1102=1900+836d/4

1102×4=1900+863d

4408=1900+863d

4408-1900=863d

2508/863=d

3=d....

Put the value of d in equation 1

So, a=(100-28d)/8

a= (100-28×3)/8

a= 16/8

a=2

In ap .. a,a+d,a+2d,a+3d

Ap= 2,5,8,11