Arithmetic progression formulas

Learn the arithmetic progression formulas one by one. Here am going to give the complete list of formulas for arithmetic sequence. Knowing the formulas of arithmetic sequence is very important for solving problems on A.P. Before solving any problem we have check the given sequence is in which progression. For this also you have to learn arithmetic progression formulas. Below listed are the some important arithmetic progression formulas:

Notation of terms in Arithmetic progression:

a, a + d, a + 2d, a + 3d, a + 4d, ………………………………………………..a + (n-1)d.

Here

a = first term of Arithmetic progression.

n = number of terms in Arithmetic progression.

d = common difference.

Common difference of A.P:

Common difference is represented by ‘ d ‘

Therefore

d = tn+1 – tn

General nth term of Arithmetic progression:

Tn = a + (n-1) d.

nth term is also called as last term in the given sequence or progression.

So now we can write the nth of an Arithmetic progression as,

l = Tn = a + (n-1) d.

Arithmetic Mean (A.M):

If a, b, c are any three terms in Arithmetic progression, then

‘b’ is called Arithmetic mean between ‘a’ and’ c’.

Therefore

b = a + c/2

Sum of n terms of Arithmetic progression:

sn = n/2 [ 2a + (n -1) d ]

or

sn = n/2 [ a + l]   where a = first term of A.P and l = last term of A.P.

Properties of Arithmetic progression:

If we add a non zero number to the all terms of A.P then the resultant sequence is also will be Arithmetic progression.

If we subtract a non zero number from all terms of A.P then the resultant sequence is also will be Arithmetic progression.  If we multiply a non zero number with all terms of A.P then the resultant sequence is also will be Arithmetic progression.

If we divide all the terms of A.P with a non zero number then the resultant sequence is also will be Arithmetic progression.

These are the minimum formulas you have to remember in Arithmetic progression. I hope this formulas are enough to attempt any problem based on Arithmetic progression. 