Question

IX=
11 The common difference of two different arithmetic progressions are equal
The first term of the first AP is 3. More than the first term of second
progression. If the 7 term of first progression is 28 and 8 term of second
progression is 29. Then find the different arithmetic progressions​

Answer 1

For the second progression,

an2=a+(n2-1)d...(I)

According to the question,

an1=3+a+(n2-1)d

an1=3+an2...(i)

And it also says,

a7=a+6d

a+6d=28...(ii)

a+7d=29...(iii)

Solving (iii) and (ii),we get

d=1

Putting d in (ii),

a+6=28

a=22

an2=22+(n2-1)d

and from (i),

an1=3+22+(n1-1)d

an1=25+(n1-1)d