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.
If the sequence is non-linear, you need to establish how it is defined.
It is the sequence of first differences. If these are all the same (but not 0), then the original sequence is a linear arithmetic sequence. That is, a sequence whose nth term is of the form t(n) = an + b
There are infinitely many possible answers. The simplest, linear, rule is Un = 4n - 17 for n = 1, 2, 3, ...
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.
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
If the sequence is non-linear, you need to establish how it is defined.
It is the sequence of first differences. If these are all the same (but not 0), then the original sequence is a linear arithmetic sequence. That is, a sequence whose nth term is of the form t(n) = an + b
You need the rule that generates the sequence.