Question

Justify if the series $2,22,23,24,...$ form an AP ?

Answer 1

Determine if the series $2,22,23,24,...$ form an AP

Definition:

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 in the form, $2,22,23,24,...$.

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

Then, $a_1=2,a_2=22,a_3=23,a_4=24$.

The difference in first two consecutive term is $a_2-a_1=22-2=20$.

The difference in third and second term is $a_3-a_2=23-22=1$.

The differences in forth and third term is $a_4-a_3=24-23=1$

The difference in each of consecutive terms are $20,1,1$, that is not all same.

Hence, the given sequence does not form an AP.