The common difference of two different arithmetic progressions are equal.The first term of the first progression is 3 more than the first term ofsecond progression. If the 7 th term of first progression is 28 and 8 th term of second progression is 29, then find the both different arithmetic progressions

Let first term of first progression be a
And the first term of second progression be A
As per question : a=A+3 , and difference is same in both AP
And, seventh term=28(of first ap)
So, a+6d
We know a=A+3
So, a+6d..will become .A+3+6d=28
A+6d=25——(1)
And eight term =29(of second ap)
So, A+7d=29—–(2)

By elimination method in eq(1),(2)
A+6d=25—(1)
A+7d=29—(2)
————————-
-1d=-4
d=4.

Consider eq(1)
A+6d=25
A+6(4)=25
A+24=25
A=25-24
A=1

We know, a=A+3
a=1+3
a=4

1st AP : a+d, a+2d, a+3d, a+4d…
4 , 8 , 12 , 16……..
2nd AP : A+d, A+2d, A+3d, A+4d….
1 , 5 , 9 , 13…….