Question

Which of the following is true in the case of an arithmetic progression?

• A. The ratio of any two consecutive terms of the series is to be constant.
• B. The difference between any two consecutive terms of the series is to be constant.
• C. The product of any two consecutive numbers of the series is to be constant.
• D. The sum of any two consecutive terms of the series is to be constant.

Answer 1

The correct option is B

The difference between any two consecutive terms of the series is to be constant.

Let $a_1,a_2,a_3,a_4,a_5,...$ be a sequence.

For this sequence to be an AP, the difference between any two of its consecutive terms should be a constant.

$\therefore a_2–a_1=a_3–a_2=a_4–a_3=d,$

where $d$ is called the common difference of the AP.

$⟹a_2=a_1+d$

So, the given AP can also be represented in the form
$a_1,a_1+d,a_1+2d,...$