#All ABOUT AP

Arithmetic Progression:- 

Arithmetic Progression is a sequence in which common difference is constant.
e.g:- 1,2,3,4,5,6,7
Here the common difference is 1.

Consider a series 4,8,12,16,20,.............84
First term = 4
Last term = 84
Common difference = 4

General term of AP is defined as,
first term + (number of terms - 1)*Common Difference
Tn = a + (n - 1)*d

From the above sequence,
a = 4
Tn = 84
d = 4
Let's find the number of terms in the above sequence
84 = 4 +(n - 1)*4
4*n = 84
n = 21

Sum of AP:-
[[[        Sn = n/2(2a +(n - 1)*d)       ]]]

Now,
Sn = n*(a + [(n-1)/2]*d)
[[[       Sn = n*Middle term      ]]]

Arithmetic Mean(AM):-

if the numbers are in AP then Arithmetic mean is nothing but the middle term(if the number of terms is odd).
On the other hand, arithmetic mean is nothing but the average of the numbers.
i.e, Sum of numbers/Total numbers
e.g:- 1,3,5,7,9
AM = (1+3+5+7+9)/5 = 5
On the other hand if we look it as an AP then we can directly say that AM is 5.



Question- Is the sequence 1,1,1,1,1,1,1,1,1,1,1 is an AP?