Two APs have the same common difference. The first term of one of these is –1 and that ofthe other is – 8. The difference between their 4th terms is

The problem involves two arithmetic progressions (APs) with the same common difference.

The first term (a1) of the first AP is -1 and the first term (a2) of the second AP is -8.

The nth term of an AP is given by the formula: a + (n-1)d, where a is the first term and d is the common difference.

So, the 4th term of the first AP (let's call it t1) is: -1 + 3d (because n=4 so n-1=3).

The 4th term of the second AP (let's call it t2) is: -8 + 3d.

The difference between their 4th terms is t1 - t2 = (-1 + 3d) - (-8 + 3d).

The 3d in both terms will cancel out because they are the same in both APs, leaving us with -1 - (-8) = 7.

So, the difference between the 4th terms of the two APs is 7.