The list of numbers \(-10,-6,-2,2,\ldots\) is
an AP with \(d=-16\)
an AP with \(d=4\)
an AP with \(d=-4\)
not an AP
Step 1: Write the numbers clearly: \(-10, -6, -2, 2, \ldots\)
Step 2: In an Arithmetic Progression (AP), the difference between one number and the next must be the same each time. This difference is called the common difference (\(d\)).
Step 3: Find the difference between the second and the first number: \(-6 - (-10) = -6 + 10 = 4\).
Step 4: Find the difference between the third and the second number: \(-2 - (-6) = -2 + 6 = 4\).
Step 5: Find the difference between the fourth and the third number: \(2 - (-2) = 2 + 2 = 4\).
Step 6: Since the difference is the same (\(4\)) every time, the numbers form an AP with common difference \(d = 4\).
Final Answer: The list is an AP with \(d = 4\). (Option B)