The properties of sequences or arithmetic series

Characteristics of Rows or Arithmetic Rows [1945909] [1945907] has given an explanation of Lineage and Arithmetic Arrangements to complete the post, This time will be discussed about the properties possessed by sequence or arithmetic series. You must look again at the concepts of the n and the n first tribes in the arithmetic series. If you have understood it well, then surely you will be able to understand the properties that apply to the sequence or the following series of arithmetic more easily:

Nature -The Characteristics of the Row or Arithmetic Arranges


First Nature:
If x, y, and z are consecutive numbers From a row of arithmetic, it will apply:

"Twice the middle number equals the sum of the two numbers that are next to it"

2y = x + z

Proof:
Let's say an arithmetic sequence has different b then y = x + b and z = x + 2b so:

2y = x + z [1945909]
2 (x + b) = x + (x + 2b)
2x + 2b = 2x + 2b
Proved that the right-hand side = left-hand

[1945909]
Second Nature:
When w, x, y, z four consecutive numbers of An arithmetic sequence, would apply:

"The sum of the two numbers that lie in the center is equal to the sum of the two numbers that are beside it"

x + y = w + z [1] [1945907]
Proof:
Suppose an arithmetic sequence Have different b then x = w + b y = w + 2b, z = w + 3b thus:

x + y = w + z
(w + b) + (w + 2b) = w + (w + 3b)
2w + 3b = 2w + 3b

Proven that the right-hand side = the left-hand


Third Property:
Apaila U is the ninth tribe N arithmetic sequence is then applicable:

"The difference between the number of n The first tribe and number n - 1 the first tribe is the tribe n "
Source: Salamah. U. 2012. Berlogika dengan Matematika 3. Solo: Platinum

So many discussions and brief explanations of the matter Or Arithmetic Arranges learn well these traits because if you can understand them well then it will be easier for you to solve the problems related to the row material and arithmetic series.
[1945909]

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