Two APs have the same common difference. The first term of one is \(-1\) and of the other is \(8\). Then the difference between their 4th terms is
−1
−8
7
−9
Step 1: The formula for the \(n^{th}\) term of an AP is:
\(a_n = a + (n-1) \times d\)
Step 2: For the first AP, the first term \(a = -1\) and the common difference is \(d\).
So, the 4th term = \(-1 + (4-1) \times d = -1 + 3d\).
Step 3: For the second AP, the first term \(a = 8\) and the common difference is the same \(d\).
So, the 4th term = \(8 + (4-1) \times d = 8 + 3d\).
Step 4: Now, find the difference between the 4th terms:
\((-1 + 3d) - (8 + 3d) = -1 + 3d - 8 - 3d = -9\).
Step 5: Therefore, the difference between their 4th terms is \(-9\).