Question

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

Answer 1

Determine if the series $-1,-1,-1,-1,...$ 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 in the form, $-1,-1,-1,-1,...$.

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

Then, $a_1=-1,a_2=-1,a_3=-1,a_4=-1$.

The difference in first two consecutive term is $a_2-a_1=-1-\left(-1\right)=-1+1=0$.

The difference in third and second term is $a_3-a_2=-1-\left(-1\right)=-1+1=0$.

The difference in forth and third term is $a_4-a_3=-1-\left(-1\right)=-1+1=0$..

Since, the difference in each of consecutive terms are same and is equal to zero.

Therefore, the given sequence form an AP.