Question

2 ap's 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 21 st terms ,which is the same as the difference between any two corresponding terms.Why?

Answer 1

Let the same common difference of two ap`s is, 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 term of the first and second AP's are 2 + 9d, and 7+ 9d, respectively.

So their difference is 7 +9d - (2 + 9d) =5

Also, 21st term of first and second AP's are 2 +20d and 7+ 20d, respectively.

So their difference is 7+ 2d - (2+ 9d) =5

Also, if the a,, and the bn are the nth term of first and second AP.

Then, bn - an= [7 +(n-1)d] - [2+(n-1)] =5

Hence, the difference between any two corresponding terms of such AP's is the same difference between their first term.