Two 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 21st terms, which is the same as the difference between any two corresponding terms? why?


Suppose there are two AP's with first terms a and A


And their common differences are d and D respectively


Suppose n be any term


an = a + (n - 1)d


An = A + (n - 1)D


As common difference is equal for both AP's


We have D = d


Using this we have


An - an = a + (n - - 1)d - [ A + (n - 1)D]


= a + (n - 1)d - A - (n - 1)d


= a - A


As a - A is a constant value


Therefore, difference between any corresponding terms will be equal to a - A.


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