Question

the sum of first 8 terms of an ap is hundred and the sum of its first and 19 terms is 551 find the AP​

Answer 1

Answer:

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

First we will list the data we are given.

The sum of the first 8 terms of the A.P is =

100

.

The sum of the first 19 terms is =

551

.

Now Let The First term of the A.P be

a

and the common difference be

d

So, According to the problem,

×

x 82[a+a+(8−1)d]=100

⇒4[2a+7d]=100

⇒2a+7

And,

192[a+a+(19-1)d]=551

⇒192[2a+18d]=551

⇒19[a+9d]=551

⇒a+9d=29

Now, Just Solve For

a and d.

FIrst, Multiply (ii) with

2

.

So, we get,

2a+18d=58

Now. Subtract (i) from (iii).

So, We get,

×

x 2a+18

d−2a−7

d=58−25

⇒11d=33

⇒d=3

Now, Substitute

d=3

in (i).

So, We get,

×

x2a+7⋅3=25

⇒2a+21=25

⇒2a=25−21

⇒2a=4

⇒a=2

So, Now we can form the A.P.

The AP will be

a,a+d,a+2d,a+3d

,a+(n−1)d

So, The Finalised A.P. is :-

2,5,8,11,14