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An arithmetic progression is a sequence of numbers where the difference between consecutive terms is constant. The nth term of an arithmetic progression can be calculated as a+(n-1)d, where a is the first term, d is the common difference, and n is the term number. Some examples of arithmetic progressions include the sequence of odd numbers (with common difference of 2) and multiples of 3 (with common difference of 3). Formulas are also provided to calculate the nth term and sum of terms for an arithmetic progression.
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Sequences
Sequences represent ordered lists of elements and can be defined as a function from a subset of natural numbers to a set. There are two main types of sequences: arithmetic sequences, where each term is obtained by adding a common difference to the previous term, and geometric sequences, where each term is obtained by multiplying the previous term by a common ratio. Mathematical induction can be used to prove properties are true for all terms in a sequence by showing the base case holds and the inductive step follows from the assumption.
Arithmetic Progression - $@mEe
An arithmetic progression is a sequence of numbers where the difference between consecutive terms is constant. The document provides examples of arithmetic progressions and discusses formulas for calculating the nth term in a sequence, the sum of terms in a finite arithmetic progression, and solving problems involving finding the number of terms, first term, or common difference given values in the sequence.
Sequence and Series
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sequence and series.docx
The document defines and describes different types of sequences, including arithmetic, harmonic, and geometric sequences. It also discusses the convergence properties of sequences, defining convergent, divergent, and oscillating sequences. Some techniques for evaluating limits of convergent sequences are presented, including using continuous function representations and properties of polynomials.
Series in Discrete Structure || Computer Science
The document defines and provides examples of sequences, series, arithmetic progressions, and geometric progressions. It gives the formal definitions and notations used to represent these concepts. Several examples are worked through to demonstrate finding explicit formulas for sequences based on given terms, computing specific terms of sequences, and identifying terms of sequences based on given properties like the first term, common difference or ratio, and a target term value.
Arithmetic Sequences and Series-Boger.ppt
The document discusses arithmetic sequences and series. Some key points include:
- An arithmetic sequence is a sequence whose consecutive terms have a common difference. The common difference is the number added to get the next term.
- An arithmetic series is the sum of terms in an arithmetic sequence.
- The formula to find any term in an arithmetic sequence is an = a1 + (n - 1)d, where a1 is the first term, n is the term number, and d is the common difference.
- The formula to find the sum of the first n terms of an arithmetic sequence is Sn = (n/2)(a1 + an), where a1 is the first term, an is the last
Arithmetic Sequences and Series-Boger.ppt
The document discusses arithmetic sequences and series. Some key points include:
- An arithmetic sequence is a sequence whose consecutive terms have a common difference. The common difference is the number added to get the next term.
- An arithmetic series is the sum of terms in an arithmetic sequence.
- Formulas are provided for finding the nth term of an arithmetic sequence and the sum of the first n terms of an arithmetic sequence.
- Examples are given of finding terms, common differences, and sums of arithmetic sequences and series.
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Ap presentation
- 1. PROGRESSION
- 2. In mathematics, an arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. The nth term of an ap is a+(n-1)d where a=first term , d=common difference , n= num of terms
- 3. 1. The sequence of odd numbers eg : 1,3,5,7 … Here, the difference between each successive term is 2.So the sequence has common difference 2 2. 3,6,9,12… Here the sequence is the multiples of 3. Here too , there is a common difference which is 3 So, these 2 sequences can said to be in Arithmetic progression
- 4. 1. n th term = a +(n-1)d 2. Sn = n/2 {2a + (n-1)}d where sn – the sum of n terms
- 5. The common difference of an ap is 7.The 11 term is 94.what will be the first term of the sequence? Find the sum of 1o terms of ap having 1st term 6 and common difference 3? If the nth term of an ap is 34.given a=22 and d=3.Find n?