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Power Sequences :

The  Power sequence constructor proceeds a formation comprise the enumerated sequences of a given formation R; it is primarily helpful as a parent for supplementary set  and sequence constructors. The single operation to facilitate acceptable on power sequences are printing, testing constituent link, and compulsion into the power sequence

Designing the power sequence:

The entire excess sequences are derivative of the power sequence. Generally the factor of the power is comparatively small periods of sequences to large powers.

Square of positive integers:  1² 2² 3² 4² 5²

Square sequence :    1     4         9        16      25

In the power of sequence we can compute the all consecutive term by raising uninterrupted positive integers to the similar power. The sequence of the power 2 and the sequence of the power three are the two frequent power sequences.

Numeric Sequence :

The numeric sequences always contain one number series,  examples of numeric sequaences are given below.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ….etc the constant numeric sequences value is one

15, 17, 19, 21, 23, 25, 27, 29…..etc. the constant numeric sequences value is one

The above examples are simple explanation of the numeric sequence.

Different types of numeric sequences are :

• Arithmetic sequence
• Geometric sequence
• Fibonacci Sequence

Numeric Sequence :

The numeric sequence is called linear sequence. The numeric sequence  are communicated to the constant rates of change and form straight lines are graphed.

The numeric sequence are  15, 17, 19, 21, 23, 25… is a linear sequence are represent in the table .the numeric sequence is used to draw graph they provide straight line.

Example:

15, 17,19,21,23 this example numeric sequence the constant value  is 2.

The sequence which is described to represent its first terms and the formula is to determine the other terms of the sequences such a formula is called as recursive formula .For example, 1, 4, 5, 9, 14, …, are the sequences because each term is obtained by taking the sum of preceding two terms .The corresponding recursive formula is a_{n + 2} = a_n + a_{n + 1} , n ≥ 1 here a₁ = 1, a₂ = 4,a₃ = 5.

Terms of a sequences:

The various numbers which occurs in the sequences are called its terms. We represents the terms of the sequences by a_1, a₂, a₃, … an the subscript denote the position of the term. The nth term is called the general term of the sequence.. The word ‘sequence’ is used as in the common use of the term to convey the idea of a set of things in order.

For example, in the sequence 1, 3, 5, 7… 2n-1 the 1st term is 1, 2nd term is 3 and nth term is 2n − 1.

Every number after the second is obtained by the sum of the previous two terms.

V₁ = 1

V₂ = 1

V₃ = V₂ + V₁

V₄ = V₃ + V₂

V_n = V_{n − 1} + V_{n − 2}

V_n = V_{n − 1} + V_{n − 2}.This sequence is called Fibonacci sequence.

Introduction of sequences,

A sequence is a function from the group of natural numbers to the group of real numbers .

The sequence  is represented by the letter a, where the image of ‘n’ belongs to the integer number ‘N’ under the sequence ‘a’ is a(n) = an. Since the domain for every sequence is the set of natural numbers, like 1, 2, 3, … n under the sequence.Here a_1, a₂, a₃ … an form the sequence.