Find a recursive formula for the sequence:
1, -1, -7, - 25
To find a recursive formula for a sequence, we need to look for a pattern in the terms of the sequence. Let's analyze the given sequence: 1, -1, -7, -25.
If we observe the differences between consecutive terms, we see that the pattern is as follows:
-1 - 1 = -2
-7 - (-1) = -6
-25 - (-7) = -18
We notice that the differences are decreasing by 2 each time. This suggests that the recursive formula will involve subtracting 2 from the previous term.
Let's denote the n-th term of the sequence as a_n. We can express the recursive formula as:
a_n = a_{n-1} - 2
To determine the initial term or the base case, we can observe that the first term, a_1, is 1.
Therefore, the recursive formula for the given sequence is:
a_n = a_{n-1} - 2, with a_1 = 1