Two arithmetic progressions have the same common difference. The first term of one A.P is $-5$ and that of the other is $-9$. Find the difference between their $7^{th}$ terms.
Let common difference $= d$
Case 1: First term $= a = -5$
$\therefore$ $7^{th}$ term $= t_7 = a + 6d = -5 + 6d$
Case 2: First term $= A = -9$
$\therefore$ $7^{th}$ term $= T_7 = A + 6d = -9 + 6d$
$\therefore$ Difference between the two $7^{th}$ terms $= t_7 - T_7 = -5 + 6d - \left(-9+6d\right) = -5+6d+9-6d = 4$