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(a) 1 (b) -7 (c) 7 (d) 9

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 start with the first AP. We are given that the first term is -1. Since the common difference is the same for both APs, we can use this information to find the terms of the second AP.

The common difference is the difference between consecutive terms in an AP. So, if the first term of the first AP is -1 and the first term of the second AP is -8, the common difference is -8 - (-1) = -7.

Now, let's find the 4th term of each AP.

For the first AP, we can use the formula for the nth term of an AP: an = a1 + (n-1)d, where an is the nth term, a1 is the first term, n is the position of the term, and d is the common difference.

For the first AP, a1 = -1 and d = -7. Plugging these values into the formula, we get a4 = -1 + (4-1)(-7) = -1 + 3(-7) = -1 - 21 = -22.

For the second AP, a1 = -8 and d = -7. Using the same formula, we get a4 = -8 + (4-1)(-7) = -8 + 3(-7) = -8 - 21 = -29.

Finally, we can find the difference between the 4th terms of the two APs by subtracting the second AP's 4th term from the first AP's 4th term: -22 - (-29) = -22 + 29 = 7.

Therefore, the difference between the 4th terms of the two APs is 7. So, the correct answer is (c) 7.