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A series is a special case of a sequence where the n'th term is the sum of n numbers a1, a2, ..., an. In other words, it is a sequence in the form S1 = a1 S2 = a1 + a2 S3 = a1 + a2 + a3 ... Sn = a1 + a2 + ... + an

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What does summation of infinite series?

The summation of a geometric series to infinity is equal to a/1-rwhere a is equal to the first term and r is equal to the common difference between the terms.


Which number should come at the end of the series 1 4 9 16?

The next number is 25 but there are the sequence is infinite so there can be no end to the sequence.


Is 0.21525 geometric or arithmetic?

The term "0.21525" itself does not indicate whether it is geometric or arithmetic, as it is simply a numerical value. To determine if a sequence or series is geometric or arithmetic, we need to examine the relationship between its terms. An arithmetic sequence has a constant difference between consecutive terms, while a geometric sequence has a constant ratio. If you provide a series of terms, I can help identify its nature.


What is a non example of arithmetic sequence?

A non-example of an arithmetic sequence is the series of numbers 2, 4, 8, 16, which is a geometric sequence. In this sequence, each term is multiplied by 2 to get to the next term, rather than adding a fixed number. Therefore, it does not have a constant difference between consecutive terms, which is a defining characteristic of an arithmetic sequence.


What is the difference between an arithmetic and geometric sequence?

An arithmetic sequence is a series of numbers in which each term is obtained by adding a constant value, called the common difference, to the previous term. In contrast, a geometric sequence is formed by multiplying the previous term by a constant value, known as the common ratio. For example, in the arithmetic sequence 2, 5, 8, 11, the common difference is 3, while in the geometric sequence 3, 6, 12, 24, the common ratio is 2. Thus, the primary difference lies in how each term is generated: through addition for arithmetic and multiplication for geometric sequences.

Related Questions

What is the difference between an arithmetic series and an arithmetic sequence?

An arithmetic sequence is a list of numbers which follow a rule. A series is the sum of a sequence of numbers.


What does summation of infinite series?

The summation of a geometric series to infinity is equal to a/1-rwhere a is equal to the first term and r is equal to the common difference between the terms.


Which number should come at the end of the series 1 4 9 16?

The next number is 25 but there are the sequence is infinite so there can be no end to the sequence.


How can you tell if a infinite geometric series has a sum or not?

The geometric series is, itself, a sum of a geometric progression. The sum of an infinite geometric sequence exists if the common ratio has an absolute value which is less than 1, and not if it is 1 or greater.


Is 0.21525 geometric or arithmetic?

The term "0.21525" itself does not indicate whether it is geometric or arithmetic, as it is simply a numerical value. To determine if a sequence or series is geometric or arithmetic, we need to examine the relationship between its terms. An arithmetic sequence has a constant difference between consecutive terms, while a geometric sequence has a constant ratio. If you provide a series of terms, I can help identify its nature.


Is 1 1 1 1 1 an arithmetic sequence?

Yes, with a difference of zero between terms. It is also a geometric series, with a ratio of 1 in each case.


What is the difference between the N series and C series nokia mobile phones?

what is the difference between N series and C series in nokia mobile phones


What is a non example of arithmetic sequence?

A non-example of an arithmetic sequence is the series of numbers 2, 4, 8, 16, which is a geometric sequence. In this sequence, each term is multiplied by 2 to get to the next term, rather than adding a fixed number. Therefore, it does not have a constant difference between consecutive terms, which is a defining characteristic of an arithmetic sequence.


What is the pattern of these numbers '1 1 2 3 5 8 13 21'?

Each new number in the series is the sum of the previous two numbers. That sequence is part of an infinite series called the Fibonacci series.


What is the difference between series and parralal circuit?

difference between series is one pathway through circuit,difference between parralal is more then one pathway through circuit.


What is the difference between successive terms?

The difference between successive terms refers to the change or gap in value between consecutive elements in a sequence or series. It is calculated by subtracting the earlier term from the later term. For example, in the sequence 2, 5, 9, the differences between successive terms are 3 (5 - 2) and 4 (9 - 5). This concept is often used in analyzing patterns or trends in mathematical sequences.


Can difference between AP series and GP series?

Succession of numbers of which one number is designated as the first, other as the second, another as the third and so on gives rise to what is called a sequence. Sequences have wide applications. In this lesson we shall discuss particular types of sequences called arithmetic sequence, geometric sequence and also find arithmetic mean (A.M), geometric mean (G.M) between two given numbers. We will also establish the relation between A.M and G.M