Arithmetic Sequence Calculator

Arithmetic Sequence

a_n = first term + a_(n-1) * d

A sequence is defined as arithmetic seqeunce "if the differences between the two consecutive term is same(constant)". Also, in the arithmetic sequence, by adding a fixed number to the previous term every term is obtained.
For example: 2,4,6,8,10,12..... is an arithmetic sequence.

Arithmetic Sequence Formula

Let us assume the first term of an arithmetic sequence is a, its common difference is d and n is the number of terms. Then the general form of the AP is a, a+d, a+2d, a+3d,......up to n terms. There are different formulas associated with an arithmetic sequence used to calculate the nth term, the sum of n terms of an AP, or the common difference of a given arithmetic sequence.

• common difference(d) = a₂ - a₁
• n^th term = a+ a_n-1 x d
• sum of n terms = (n/2) (2a + (n-1) x d)
  OR [a1+a_n] x d

Arithmetic Sequence Example

Consider the sequence 2, 4, 6, 8, 10, .... is an arithmetic sequence because every term is obtained by adding a constant number (2) to its previous term.

Thus, an arithmetic sequence can be written as a, a + d, a + 2d, a + 3d, ....
Let's calculate the above example:
a, a + d, a + 2d, a + 3d, a + 4d, ... = 2, 2 + 2, 2 + 2(2), 2 + 2(3), 2 + 2(4),... = 2, 4, 6, 8, 10, 12.............