Question

The sum of the 3rd and the 7th of an A.P. is 4, where as the sum of
the 5th and 9th terms is 24. Find the
first three terms of A.P.​

Answer 1

Answer:

an=a+(n-1)d

so,3rd term = a+2d

7th term = a+6d

The sum of 3rd term and 7th term is 54

a+2d+a+6d=54

2a+8d=54

a+4d=27 ____________1

Now, 5th term = a+4d

And 11th term = a+10d

The sum of 5th and 11th term is 84

a+4d+a+10d=84

2a+14d=84

a+7d=42 ________________2

sub. 1 from 2, we get

3d=15

d=15/3

d=5

putting value of d in 1

a+4(5)=27

a+20=27

a=27-20

a=7

1st term=7

2nd term= a+d=7+5=12

3rd term= a+2d=7+2(5)=17

4th term= a+3d=7+3(5)=22

Now the A.P is

7, 12, 17, 22, …………………

Answer 2

Answer:

Check the picture, the steps are written.