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
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.
You need the rule that generates the sequence.
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
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.