The general rule for the nth term of the sequence is [tex]a(n)=-6b+(n-1)(3b)[/tex]
Explanation:
The sequence is -6b, -3b, 0b, 3b, 6b, .....
To find the nth term of the sequence, we need to find the common difference and the first term of the sequence.
First term of the sequence = -6b
Common difference = [tex]-3b-(-6b)=-3b+6b=3b[/tex]
Using this the nth term of the sequence can be determined.
Since, this is an arithmetic sequence, the general form of AP is given by the formula,
[tex]a(n)=a+(n-1)d[/tex]
where a denotes the first term of the sequence and d denotes the common difference. Thus, [tex]a=-6b[/tex] and [tex]d=3b[/tex]
Substituting the values in the general formula, we get,
[tex]a(n)=-6b+(n-1)(3b)[/tex]
Thus, the general rule for the nth term of the sequence is [tex]a(n)=-6b+(n-1)(3b)[/tex]
