Question

Justify if the series $1,1,2,2,3,3...$ form an AP ?

Answer 1

Determine if the series $1,1,2,2,3,3...$ form an AP

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

Check if the series form an AP:

The given series is, $1,1,2,2,3,3...$.

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

Then, $a_1=1,a_2=1,a_3=2,a_4=2,a_5=3,a_6=3$.

The difference in first two consecutive term is $a_2-a_1=1-1=0$.

The difference in third and second term is $a_3-a_2=2-1=1$.

Since, the difference in the two consecutive term, $a_2-a_1\ne a_3-a_2$, no need to find further difference.

Hence, it is concluded that the sequence does not form an AP.