# . Two APs have the same common difference The first term of one AP is 2 and that of the other is 7

The difference between their 10th terms is the same as the difference between their 21st terms,

which is the same as the difference between any two corresponding terms.If true then enter 1 and if false then enter 0.

Explanation: Given two APs with the same common difference.

Let the common difference be d.

The first term of the first AP is 2.

The first AP will be 2,2 + d,2 + 2,.....

And the first term of the second AP is 7.

The second AP will be 7,7 + d,7 +2d,...

We know that, an= a+(a - 1) d

So,10th  term of the first AP =2 + 9d

And the 10th term of the second AP 7+ 9d

Thus, the difference of their 10th  term

=( 7 +9d ) - ( 2 + 9d )

= 7 +9d - 2 - 9d

= 5

And 21st term of the first AP = 2 + 20d

21st term of the second AP 7+ 20d

So,  the difference of their 21st  term =( 7 + 20d ) - ( 2+ 20d ) = 5

Thus, if aand aare nth terms of first and second AP respectively, then Hence the difference between any two corresponding terms of such APs is the same as the difference between their first terms.

So, it is true, then enter 1.

Final Answer: The difference between any two corresponding terms of such APs is the same as the difference between their first terms. And it is true, enter 1.