Question -
Answer -
Let the same commondifference of two A.P.’s is d.
Given that, the first term of first A.P. and second A.P. are 2 and 7respectively,
then the A.P.’s are 2, 2 + d, 2 + 2d, 2 + 3d, … and 7, 7 + d, 7 + 2d, 7 + 3d, …
Now, 10th terms of first and second A.P.’s are 2 + 9d and 7 + 9d, respectively.
So, their difference is 7 + 9d – (2 + 9d) = 5
Also, 21st terms of first and second A.P.’s are 2 + 20d and 7 + 20d,respectively.
So, their difference is 7 + 20d – (2 + 9d) = 5
Also, if the an and bn are the nth terms offirst and second A.P.
Then bn – an = [7 + (n – 1 ) d] – [2 + (n – 1)d = 5
Hence, the difference between any two corresponding terms of such A.P.’s is thesame as the difference between their first terms.