The sequence you've provided, 4, 1, -2, appears to be an arithmetic sequence where each term differs from the previous term by a constant value. To find an explicit formula for the nth term (An), we can determine the common difference (d) between terms and then express the nth term in terms of n.
Common difference (d):
d = Second term - First term = 1 - 4 = -3
d = Third term - Second term = (-2) - 1 = -3
The common difference is -3, which means each term is decreasing by 3 from the previous term.
Now, to find the explicit formula for the nth term (An), we can use the following formula for arithmetic sequences:
An = A1 + (n - 1) * d
In this formula:
- An is the nth term.
- A1 is the first term (4 in this case).
- n is the term number.
- d is the common difference (-3 in this case).
So, the explicit formula for the nth term (An) of the sequence 4, 1, -2 is:
An = 4 + (n - 1) * (-3)
You can simplify this formula as:
An = 4 - 3n + 3
An = -3n + 7
So, the explicit formula for the nth term is An = -3n + 7.