Two A.P have the same common difference. The first term of one A.P is 2 and that of the other is 7. The difference between the 10th terms is the same as the difference between their 21st terms, which is the same as the difference between any corresponding terms. Why?

Explanation

Let the same common difference of two AP's is d. Given that, the first term of first AP and second AP are 2 and 7 respectively, then the AP's are
` " " 2, 2 + d,2+2d,2+3d, …`
and `7, 7+d,7+2d,7+3d, …`
Now, 10th terms of first and second AP's are `2+9d` and `7+9d`, rspectively.
So, their difference is `7+9d-(2+9d)=5`
Also, 2 1st terms of first and second AP's are `2+20d` and `7+20d`, respectively.
So, their difference is `7+20d-(2+9d)=5`
Also, if the `a_(n)` and `b_(n)` are the nth terms of first and second AP.
Then `b_(n)-a_(n)=[7+(n-1)d]-[2+(n-1)d]=5`
Hence, the difference between any two corresponding terms of such AP's is the same as the difference between their first terms.