Answer:
Explanation:
This is an arithmetic sequence with a common difference of -12. To find the recursive formula, let's start by finding a general formula for the nth term.
Let a be the first term (3 in this case) and d be the common difference (-12 in this case). The nth term of the sequence can be found using the formula:
an = a + (n-1)d
Using this formula, the first four terms of the sequence are:
a1 = a + (1-1)d = 3 + (1-1)(-12) = 3
a2 = a + (2-1)d = 3 + (2-1)(-12) = 3 - 12 = -9
a3 = a + (3-1)d = 3 + (3-1)(-12) = 3 - 24 = -21
a4 = a + (4-1)d = 3 + (4-1)(-12) = 3 - 36 = -33
So, the sequence is: 3, -9, -21, -33, ...
We can now use this information to write the recursive formula for the sequence:
an = a(n-1) + d
So, for the sequence 3, -9, -21, -33, ... the recursive formula is:
an = an-1 + (-12)
This formula tells us how to find the nth term of the sequence given the (n-1)th term. The sequence starts with the first term a1 = 3 and the common difference is d = -12. By repeatedly applying the formula, we can find the values for the subsequent terms in the sequence.