Question

Indicate a general rule for the nth term of this sequence. -6b, -3b, 0b, 3b, 6b. . .

Answer 1

The general rule for the nth term of the sequence is $a(n)=-6b+(n-1)(3b)$

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 = $-3b-(-6b)=-3b+6b=3b$

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,

$a(n)=a+(n-1)d$

where a denotes the first term of the sequence and d denotes the common difference. Thus, $a=-6b$ and $d=3b$

Substituting the values in the general formula, we get,

$a(n)=-6b+(n-1)(3b)$

Thus, the general rule for the nth term of the sequence is $a(n)=-6b+(n-1)(3b)$