Arithmetic progression VS Geometric progression: ap vs gp

ap vs gp

Arithmetic progression VS Geometric progression:

1,2,3,...    VS   3,9,27,...

Let's Closely and carefully watch both series...🤫

 What did we see?

In the first series: 1,2,3...

  1, 1+1, 2+1,...and so on...

That means, adding 1 to the previous term of the series we get the next term.

Also, the series starts with 1 and two consecutive terms has a common difference of 1.

This type of series is known as Arithmetic progression (ap or, A.P.)

Now, let's go to the second series: 3,9,27,...

 3, 3×3, 9×3,...and so on...

Here, if we multiply the previous term with 3, we get the next term.

 The series starts with 3 and two consecutive terms has a common ratio 3.

This type of series is known as Geometric progression (gp or, G.P.)

 

The following image clearly and briefly reflects ap vs gp. Difference and relation between Arithmetic progression and Geometric progression: ap vs gp.

i.e., in a more general mathematical form:

 ap or A.P. or Arithmetic progression looks like:  

                      a, a+d, a+2d,...

a= first term, d= common difference.

And, gp or G.P. or Geometric progression looks like:

                       a, ar, ar×r,...

a= first term, r= common ratio.

 In brief, ap vs gp :

 ap or Arithmetic progression is related to addition of terms with a fixed number.

And, gp or Geometric progression is related to multiplication of terms with a fixed number.

Thanks.