Main Sequence

Introduction to main sequence:

A set of numbers whose domain is a real number is called a SEQUENCE and sum of the sequence is called a SERIES.

Those main sequences whose terms follow certain patterns are called progressions.

For example

·         1, 4, 7, 10, 13 …

·         7, 4, 1, – 2, – 5 …

·         1, 2, 4, 8, 16 …

·         8, 4, 2, 1, ½ …

Types of Main Sequence:

The main sequences can be classified as

There are three different progressions

·         Arithmetic Progression (A.P)

·         Geometric Progression (G.P)

Arithmetic Progression (A.P.)
It is a series in which any two consecutive terms have common difference and next term can be derived by adding that common difference in the previous term.

Geometric Progression
A series in which each preceding term is formed by multiplying it by a constant factor is called a Geometric Progression . The constant factor is called the common ratio and is formed by dividing any term by the term which precedes it.

Properties of Main Sequence:

Properties of the Main Sequence:
If each term of a main sequence is increased, decreased, multiplied or divided by the same non-zero number, then the resulting series will also be a sequence. This can be explained as  3, 5, 7, 9, 11… is a  main sequence and let each term of the sequence is increased by 5    then the new sequence will be 8, 10, 12, 14, 16 ...  will also be a new main sequence.
The difference between the two consecutive terms of the main sequence that is in AP will always remain constant.
If each term of a main sequence, which is in Geometrical progression, is multiplied or divided by the same non-zero  quantity, then the resulting sequence is also a Geometric    progression and can be classified as main sequence.
For example: For G.P. is 2, 4, 8, 16, 32… If each of the term is multiplied by 2 we get the sequence 4, 8, 16, 32,                                 64 … which is also in Geometrical progression. Please express your views of this topic math formula sheet by commenting on blog.

Questions for Practice on Main Sequence:

What will be the next two term of the main sequence 6, 17, 28, 39, __ ,  __  ?
If we add to an arithmetic progression then the new sequence will also be in AP?   (True  / False  )
The difference between the consecutive terms of main sequence which is in AP is always constant?   (True  / False)