6n-5 is the nth term of this sequence
3n - 7
It is Un = 3n - 7.
Un = 4n - 13.
The nth term is: 3n+2 and so the next number will be 20
The nth term is 2n+5 and so the next number is 17
3n - 7
It is Un = 3n - 7.
Un = 4n - 13.
The nth term is: 3n+2 and so the next number will be 20
no
The recursive rule for the sequence can be defined as follows: ( a_1 = -22.7 ) and ( a_n = a_{n-1} + 4.3 ) for ( n \geq 2 ). This means each term is created by adding 4.3 to the previous term. The sequence demonstrates a consistent linear growth.
Two key characteristics of a sequence are its order and its rule. The order refers to the arrangement of elements in a specific, often linear, progression. The rule defines how each term in the sequence is generated from the previous terms or a mathematical formula. Together, these characteristics distinguish one sequence from another and determine its overall behavior.
The sequence 1, 6, 11, 16, 21, 26 follows a linear pattern where each term increases by 5. The rule for the sequence can be expressed mathematically as ( a_n = 1 + 5(n - 1) ), where ( n ) is the term number. This means the first term (when ( n = 1 )) is 1, and each subsequent term adds 5 to the previous term.
The given linear sequence is 13, 7, 1, -5, -11, which has a common difference of -6. To find the nth term rule, we can use the formula for the nth term of an arithmetic sequence: ( a_n = a + (n-1)d ), where ( a ) is the first term and ( d ) is the common difference. Here, ( a = 13 ) and ( d = -6 ), so the nth term can be expressed as ( a_n = 13 + (n-1)(-6) ). Simplifying this gives ( a_n = 19 - 6n ).
It is not possible to answer the question since a non linear sequence could be geometric, exponential, trigonometric etc.
The nth term is 2n+5 and so the next number is 17
The position to term rule in mathematics refers to a method used to identify the terms of a sequence based on their position or index. For example, in an arithmetic sequence, the nth term can be expressed as a linear function of n, typically in the form (a_n = a + (n-1)d), where (a) is the first term and (d) is the common difference. This rule helps in finding specific terms without listing the entire sequence. It's also applicable in other types of sequences, such as geometric sequences, where the nth term is determined by a different formula.