Question

Justify if the series $1/2,1/3,1/4,...$ form an AP ?

Answer 1

Determine if the series $1/2,1/3,1/4,...$ form an AP

An AP is sequence of numbers such that the difference in each of the 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, $1/2,1/3,1/4,...$.

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

Then, $a_1=1/2,a_2=1/3,a_3=1/4$.

The difference in first two consecutive term is $a_2-a_1=1/3-1/2=-1/6$.

The difference in third and second term is $a_3-a_2=1/4-1/3=-1/12$.

Since, the difference in the two consecutive term is not same.

Hence, the sequence does not form an AP.