Solving Arithmetic Sequence

An arithmetic series is also we say it as an arithmetic sequence, it is a sequence that starts with a rigid number, a, and then each following term is establish by adding up a constant value, d, called the common difference.

Arithmetic sequence is a progression of numbers that has a stable variation between every two repeated terms. In additional words, arithmetic sequence of figures in which each term not including the initial term is the outcome of adding the same number, called the common difference.


General Form for Solving Arithmetic Sequence

Arithmetic series is the indicate sum of the terms of an arithmetic sequence.

General Form:

a, a + d, a + 2d, a + 3d + . . .

The recursive formula for an arithmetic series is written in the form,

an = an-1 + d

Here, d `->` common difference,    n `->` number of terms.

The explicit formula is also called as the closed form. The precise or closed formula for solving  an arithmetic sequence, we always use is

an = a1 + (n-1) d.

Here,   d `->` common difference,   n `->` number of terms.

Example for Solving Arithmetic Sequence

Solving whether the given sequence is arithmetic or not.

Ex:   22, 20, 18, 16, 14… . . . .

Solution: At first we have to find the difference between each pair of consecutive terms.

a2 – a1 = 20 – 22 = -2

a3 – a2 = 18 – 20 = -2

a4 – a3 = 16 – 18 = -2

a5 – a4 = 14 – 16 = -2

My forthcoming post is on Mean Value Theorem Proof and Alternate Interior Angles Examples will give you more understanding about Algebra.

Now we know that the difference between the consecutive terms is constant from the above example.

Then,the common difference between the terms is = -2, so the given sequence is arithmetic. The reason for the judgment as the given sequence is arithmetic is “The difference between the consecutive terms of the sequence is constant.

Hence the sequence is arithmetic.