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The nth term of an arithmetic sequence

= a + [(n - 1) X d]

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โˆ™ 2009-07-06 05:09:57
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Q: Rule to finding terms in a arithmetic sequence?
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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 rule is for finding terms in arithmetic sequences?

Add a constant number to one term to find the next term


What is the Th term of the arithmetic sequence given by the explicit rule?

The answer depends on what the explicit rule is!


What is position -to-term rule in maths?

It is the description of a rule which describes how the terms of a sequence are defined in terms of their position in the sequence.


A sequence of numbers that follows a rule is a what?

It is a sequence of numbers. That is all. The sequence could be arithmetic, geometric, harmonic, exponential or be defined by a rule that does not fit into any of these categories. It could even be random.


What is the definition of arithmetic sequence?

An arithmetic sequence is a group or sequence of numbers where, except for the first number, each of the subsequent number is determined by the same rule or set of rules. * * * * * The above answer is incorrect. The rule can only be additive: it cannot be multiplicative or anything else.


What does number sequence mean?

Number sequences are sets of numbers that follow a pattern or a rule. If the rule is to add or subtract a number each time, it is called an arithmetic sequence. In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members (also called elements, or terms).


What are mathamatical patterns?

Mathematical patterns are lists number that follows a certain rule and have different types. Some of these are: Arithmetic sequence, Fibonacci sequence and Geometric sequence.


How is a arithmetic sequence found?

You take the difference between the second and first numbers.Then take the difference between the third and second numbers. If that difference is not the same then it is not an arithmetic sequence, otherwise it could be.Take the difference between the fourth and third second numbers. If that difference is not the same then it is not an arithmetic sequence, otherwise it could be.Keep checking until you think the differences are all the same.That being the case it is an arithmetic sequence.If you have a position to value rule that is linear then it is an arithmetic sequence.


What is the rule for this pattern 2 6 8 14?

Without further terms in the sequence, it is impossible to determine what the rule in the sequence is.


Which rule will find the nth term of the arithmetic sequence -58 -65 -72 -86?

It appears that a number of -79 is missing in the sequence and so if you meant -58 -65 -72 -79 -86 then the nth term is -7n-51 which makes 6th term in the sequence -93


What is the difference between an explicit rule and a recursive rule?

An explicit rule defines the terms of a sequence in terms of some independent parameter. A recursive rule defines them in relation to values of the variable at some earlier stage(s) in the sequence.


How do you find the next term of a sequence number?

The first step is to find the sequence rule. The sequence could be arithmetic. quadratic, geometric, recursively defined or any one of many special sequences. The sequence rule will give you the value of the nth term in terms of its position, n. Then simply substitute the next value of n in the rule.


What make a number sequence?

A number sequence is an ordered set of numbers. There can be a rule such that the next number in the sequence can be determined by the values of some or all of the preceding terms in the sequence. However, the sequence for a random walk illustrates that such a rule is not necessary to define a sequence.


What is the definition of an arithmetic sentence?

An arithmetic sequence is a sequence of numbers such that the difference between successive terms is a constant. This constant is called the common difference and is usually denoted by d. If the first term is a, then the iterative definition of the sequence is U(1) = a, and U(n+1) = U(n) + d for n = 1, 2, 3, ... Equivalently, the position-to-term rule which defines the sequence is U(n) = a + (n-1)*d for n = 1, 2, 3, ...


What are the first fourth and tenth terms of the arithmetic sequence described by the given rule A(n) 12 plus (n-1) (3)?

A(1) = 12A(4) = 3 A(10) = -15.


Which one is a rule for the n th term of an arithmetic sequence with a8 equals 56 and d equals 5?

T(n) = 5n + 16


What has a value of the first term and the rule for finding each term based on the term before?

Any iterative sequence.


What is a recursive rule for the following arithmetic sequence 27 24 21 18 15?

U1 = 27 U{n+1} = U{n} - 3


What are the types of arithmetic sequence?

There is only one type of arithmetic sequence.The sequence may be defined by a "position-to-value" rule. This would be of the form:U(n) = a + n*dwhere a a constant which equals what the 0th term in the sequence would be,d is also a constant - the common difference between each term in the sequence and the preceding term.and n is a variable that is a counter for the position of the term in the sequence.The same sequence can be defined iteratively by:U(0) = aU(n+1) = U(n) + d for n = 1, 2, 3, ...


How can you find future terms in arithmetic sequence?

You find the position-to-value rule for the sequence. This takes the form: U(n) = a + n*d where a is a constant [ = U(0), a term calculated by moving BACK one term from the first], d is the common difference between terms, and n is the counter or index. Since both a and d are known, plugging in the value of n gives the nth term. Beware, though, that some courses teach the rule as U(n) = a' + d*(n-1) where a' is the first term.


How to find the 5th term in an arithmetic sequence using the explicit rule?

Nth number in an arithmetic series equals 'a + nd', where 'a' is the first number, 'n' signifies the Nth number and d is the amount by which each term in the series is incremented. For the 5th term it would be a + 5d


What is the general rule for the arithmetic sequence 15 12 9 6?

There are two ways to say the general rule. They both mean exactlythe same thing, and they both generate the same sequence:1). Starting with 15, each new term is 3 less than the one before it.2). The nth term of the sequence is [ 18 - 3n ] or [ 3 times (6 - n) ].


What is the rule in generating a sequence?

Anything you like. You specify whatever rule you like and the resulting set of numbers is the sequence based on that rule.


Rule that states the sequence to be used when evaluating expressions?

Q: What is the rule that states the sequence to be used when evaluating expressions? A: The rule that states the sequence to be used when evaluating expressions is know as the "order of operations."

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