Question

What are the conditions for a sequence to be an AP?

• A. Division between two consecutive numbers should be same.
• B. Difference between two consecutive numbers should be same.
• C. Multiplication between two consecutive numbers should be same.
• D. Division between two consecutive numbers should be same.

Answer 1

The correct option is B

Difference between two consecutive numbers should be same.

Let $a_1$ , $a_2$ _, $a_3$ _, $a_4$ _, $a_5$, $a_6$_, $a_7$_, $a_8$… be a sequence.

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

$a_2–a_1=a_3–a_2=a_4–a_3=d$

This difference is called the common difference of the AP and is denoted by $d$.

So an AP with the first term $a$ can also be represented in this form as well $a,a+d,a+2d,...$