Question

the sum of first 8 terms of an ap is 100 and the sum of its 19 terms is 551. find the ap​

Answer 1

Answer:

From equation 1 and 2

2a+7d=25

a+9d=29-----×2

2a+7d=25

2a+18d=58

----------------

-11d= -33

d= 3

Now,

2a+7d=25

2a+21=25

2a= 4

a= 2

Therefore,

A.P is

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

Answer 2

8/2[a+a+(8-1)d]=100

=4[2a+7d]=100

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

And 19/2[a+a+(19-1)d]=55

=19/2[2a+18d] = 551

=19[a+9d]=551

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

now just solve for a and d

first , multiply eq ii with 2

so , we get,

2A + 18 d =58..................(iii)

now subtract eq (i) from eq (iii)

so we get

2A + 18d - 2a-7d =58-25

=11d =33

=d =3

Now substitute d=3is eq(i)

so we get

2A + 7.3=25

2a+21=25

2a=25-21

2a=4

a=2

so now we can form the AP

the AP will be

a,a+d,a+2d,a+3d,.............,a+( n - 1 ) d

show the finalized ap is

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