Question

In an arithmetic series, the difference between the two consecutive terms never remains constant?

A. True
B. False

Answer 1

The statement about the arithmetic series having a constant difference between consecutive terms being false is incorrect; such a series is defined by a constant common difference. Other physics concepts like displacement plots, vector addition, and wave superposition also adhere to their respective true and false statements, often adhering to basic principles such as the Pythagorean theorem and superposition.The answer to the question is true.

Step-by-step explanation:

True or False: In an arithmetic series, the difference between the two consecutive terms never remains constant. The correct answer to this statement is B. False. By definition, an arithmetic series is characterized by a constant difference between consecutive terms, known as the common difference. For example, in the series 3, 5, 7, 9..., each term increases by 2, which is the common difference.

Regarding the questions provided as reference information:

An object moving with constant acceleration will indeed have a curved displacement versus time graph and a straight line displacement versus time squared graph, which makes the statement True.

1. We can use the Pythagorean theorem to calculate the length of the resultant vector when two vectors are at right angles to each other, making this statement True.
2. For waves, the amplitude of one wave is affected by the amplitude of another wave when they are precisely aligned, which is the principle of superposition. The statement that amplitudes of waves add up only if they are propagating in the same line is True, and that they can superimpose if their frequencies are different is also True.
3. Displacement of two persons walking in a rectangular path will be the same regardless of the order in which they walk, hence the statement comparing their displacements is False.
4. A standing wave is indeed a superposition of two identical waves, but they are traveling in opposite directions, not the same direction, making the statement as provided False.
5. In hypothesis testing for matched or paired samples, statement B and C are True because matched samples involve pairs of observations and typically involve comparing two means.