Question

Two arithmetic progressions have the same common difference. Their first terms are A and B respectively. The difference between their n^th terms is _________.

Answer 1

Let the first term of first A.P. be A and common difference be d.
And the first term of second A.P. be B and common difference be d.

n^th term of first A.P. = a_n
n^th term of second A.P. = b_n

Now,
$$\begin{gathered} a_n=A+\left(n-1\right)d \\ \mathrm{and}{b}_n=B+\left(n-1\right)d \\ \mathrm{Thus}, \\ {a}_n-b_n=A+\left(n-1\right)d-B-\left(n-1\right)d \\ =A-B \end{gathered}$$

Hence, the difference between their n^th terms is A − B.