Which of the following list of numbers forms an arithmetic progression?
(A) 1, -1, -3, -5, ........
(B) -1.2, -3.2, -5.2, -7.2, ........
(C) -2, 2, -2, 2, -2, ........
(D) \(2,\frac{5}{2},3,\frac{7}{2},........\)
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A), (B) and (D) only
A list of numbers is an arithmetic progression (AP) when every term minus the term before it gives the same number, the common difference.
(A) 1, -1, -3, -5, ........ Correct. Each term is 2 less than the one before: \(-1-1=-2\), \(-3-(-1)=-2\), \(-5-(-3)=-2\). Common difference \(-2\).
(B) -1.2, -3.2, -5.2, -7.2, ........ Correct. \(-3.2-(-1.2)=-2\), and the same for every pair. Common difference \(-2\).
(C) -2, 2, -2, 2, -2, ........ Incorrect. The differences are \(+4, -4, +4, -4\): they change sign, so there is no common difference.
(D) \(2,\frac{5}{2},3,\frac{7}{2},........\) Correct. Each term is \(\frac{1}{2}\) more than the one before (2, 2.5, 3, 3.5). Common difference \(\frac{1}{2}\).