Arithmetic Sequence and and Arithmetic Numbers

Let us learn about Arithmetic Sequence and and Arithmetic Numbers.

Before we know about Arithmetic sequence, we shall first know what is meant by a sequence; a sequence is a set of numbers that follow a pattern. We call each number in the sequence a term.

An arithmetic sequence is a sequence where each term is found by adding or subtracting the same value from one term to the next. We call this value "common sum" or "common difference"

An arithmetic sequence is a linear function. Instead of y=mx+b, we write a_n=dn+c where d is the common difference and c is a constant.

Using the above definition let us solve the Arithmetic Sequence Problems listed below.

If the first term of an arithmetic sequence is -3 and the eighth term is 11, find d and write the first 10 terms of the sequence.

In this problem,

A = -3 n = 8 A8 = 11

If these values are substituted in the formula for An, we have

11 = -3 + (8 - 1) d

11 = -3 + 7d

14 = 7d

d = 2

The first ten terms are -3, -1, 1, 3, 5, 7, 9, 11, 13, 15