Question

Two AP s have same common difference The first term of one AP is2and that of other is 7 the difference between their 21st terms which is the as the difference between any two corresponding terms why?

Answer 1

Two APs have same common difference

first term of one AP is 2 and that of other is 7

nth term of first AP will be

2 + ( n-1) d

nth term of second AP will be

7 + (n-1) d

subtracting nth term of first AP by nth term of second AP

we will have

7 + ( n-1) d - ( 2 + (n-1) d)

7 + (n-1) d - 2 - (n-1) d

= 5

It means the difference of these two AP's is constant as 5.

irrespective of the value of 'n'

Therefore the difference between any two corresponding terms of these APs will be same being 5.

it is due to the same common difference of the APs.

Answer 2

answer is provided by other users