Question

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. Why?

Answer 1

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

a_n = a + (n – 1)d

A_n = A + (n – 1)D

As common difference is equal for both AP’s

We have D = d

Using this we have

A_n – a_n = 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.