Question

Justify if the series $0,2,0,2,...$ form an AP ?

Answer 1

Determine if the series $0,2,0,2,...$ form an AP

An AP is a sequence of numbers such that the difference in each consecutive term is always the same. The general form of the sequence is $a,a+d,a+2d,a+3d,....$ . Here the difference in each consecutive term is $d$.

Check if the series form an AP:

The given series is, $0,2,0,2,...$.

Let $a_n$ represents the nth term of the given sequence.

Then, $a_1=0,a_2=2,a_3=0,a_4=2$.

The difference between the first two consecutive term is $a_2-a_1=2-0=2$.

The difference between the third and second term is $a_3-a_2=0-2=-2$.

The difference between the fourth and the third term is $a_4-a_3=2-0=2$..

Since the difference in each consecutive term is not the same.

Hence, the given sequence does not form an AP.