Answer:
a(n) = -9a + 3an
Step-by-step explanation:
The first term is -6a and the next term is found by adding 3a to it. Thus, this is an arithmetic sequence with common difference 3a.
The general arithmetic sequence formula is a(n) = a(1) + (n - 1)d, where d is the common difference. Here d = 3a.
So the general rule for the given sequence is:
a(n) = -6a + (3a)(n - 1)
But this can be simplified. Perform the indicated multiplication, obtaining:
a(n) = -6a - 3a + 3an, or
a(n) = -9a + 3an
