Question

1. -3, -12, -21, -30, ...

Explanation:

Step1: Identify the pattern

First, check the difference between consecutive terms.
\(-12 - (-3) = -9\), \(-21 - (-12) = -9\), \(-30 - (-21) = -9\). So the common difference \(d = -9\).

Step2: Find the nth term formula

For an arithmetic sequence, the nth term formula is \(a_n = a_1 + (n - 1)d\), where \(a_1\) is the first term and \(d\) is the common difference. Here, \(a_1 = -3\) and \(d = -9\).

Substitute into the formula:
\(a_n = -3 + (n - 1)(-9)\)
Simplify:
\(a_n = -3 - 9n + 9\)
\(a_n = 6 - 9n\) or \(a_n = -9n + 6\)

Answer:

The nth term of the sequence is \(a_n = -9n + 6\) (or \(a_n = 6 - 9n\))