Positive Negative Zero Sequence

Introduction for positive negative zero sequence:

In this article, we will discuss about the sequence. It has two types.

1. Arithmetic sequence and

2. Geometric sequence.

Arithmetic sequence means that, the sequence of a numbers such that the difference between two consecutive members of the sequence is a constant. Geometric sequence means that, the sequence of a numbers such that the ratio between two consecutive members of the sequence is a constant. The positive negative zero sequence formulas and example problems are given below. I like to share this Adding Positive and Negative Integers with you all through my article.

Formulas and Example Problems for Sequences:

Sequences formulas are given below.

Formula for arithmetic sequence:

nth term of the sequence : an = a1 + (n - 1)d

Series of the sequence: sn = `(n(a_1 + a_n))/2 `

Formula for geometric sequence:

nth term of the sequence: an = a1 * rn-1

Series of the sequence: sn = `(a_1(1-r^n))/(1 - r)`

Example problem 1:

Find the 10th term of the Positive arithmetic series 11, 14, 17, 20,....

Solution:

First term of the series, a1 = 11

Difference of two consecutive terms, d = 14 - 11 = 3

n = 10

The formula to find the nth term of an arithmetic series, `a_n = a_1 + (n-1)d`

So, the 10th term of the series 11, 14, 17, 20,... = 11 + (10 - 1) 3

= 11 + 9 * 3

= 11 + 27

After simplify this, we get

= 38

So, the 10th term of the sequence 11, 14, 17, 20,... is 38

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More Example Problems for Positive Negative Zero Sequences:

Example problem 2:

Find the 12th term of the negative arithmetic series -13,-15, -17, -19,.....

Solution:

First term of the series, a1 = -13

Difference of two consecutive terms, d = -15 + 13 = -2

n = 12

The formula to find the nth term of an arithmetic series, `a_n = a_1 + (n-1)d`

So, the 12th term of the series -13,-15, -17, -19,..... = -13 + (12 - 1) (-2)

= -13 + 11 * -2

= -13 - 22

After simplify this, we get

= -35

So, the 12th term of the sequence -13,-15, -17, -19,.... is -35.

Example problem 3:

Find the 14th term of the zero arithmetic series 0, 10, 20, 30, 40,...

Solution:

First term of the series, a1 = 0

Difference of two consecutive terms, d = 10 - 0 = 10

n = 14

The formula to find the nth term of an arithmetic series, `a_n = a_1 + (n-1)d`

So, the 14th term of the series 0, 10, 20, 30, 40,... = 0 + (14 - 1) (10)

= 0 + 13 * 10

= 130

After simplify this, we get

= 130

So, the 14th term of the sequence 0, 10, 20, 30, 40,... is 130

The above examples are helpful to study of positive negative zero sequences.