To find the nth term of the linear sequence -9, -5, -1, we first identify the common difference between the terms. The difference between consecutive terms is 4. The first term (a) is -9, so the nth term can be expressed as ( a_n = -9 + (n-1) \cdot 4 ), which simplifies to ( a_n = 4n - 13 ).
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 ).
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
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