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

To find the difference between the 4th terms of two arithmetic progressions (APs) with the same common difference, we need to determine the terms of each AP.

Let's denote the common difference as 'd'. The first term of one AP is -1, so the terms of this AP would be: 1st term: -1 2nd term: -1 + d 3rd term: -1 + 2d 4th term: -1 + 3d

Similarly, the first term of the other AP is -8, so the terms of this AP would be: 1st term: -8 2nd term: -8 + d 3rd term: -8 + 2d 4th term: -8 + 3d

Now, we can find the difference between their 4th terms by subtracting the 4th term of the second AP from the 4th term of the first AP: (-1 + 3d) - (-8 + 3d) Simplifying this expression, we get: -1 + 3d + 8 - 3d Combining like terms, we have: 7

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