The answer depends on what the explicit rule is!
Write the explicit formula for the arithmetic sequence.
2, -2, -6, -10, -14,
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An arithmetic sequence is a list of numbers which follow a rule. A series is the sum of a sequence of numbers.
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.
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
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).
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.
An arithmetic sequence is a list of numbers which follow a rule. A series is the sum of a sequence of numbers.
The nth term of an arithmetic sequence = a + [(n - 1) X d]
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.
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
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.
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.
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
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.
A(1) = 12A(4) = 3 A(10) = -15.
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.
A pattern that not only continue the pattern but find the value for the given term in the pattern.
Since a given sequence of numbers can be designed to follow any rule, you have to use a system of trial and error to see if you can discover the rule. Sometimes the rule is obvious, sometimes it is extremely complicated. Try to invent a rule which would produce the sequence that you observe.