Answer and step-by-step explanation:
To find the nth term of the given sequence, let's determine first what kind of sequence it is.
If it is an arithmetic sequence, let's find the common difference by subtracting a term by the previous term.
1 - 4 = -3
-2 - 1 = -3
-5 - (-2) = -3
The differences are all the same. Therefore, there is a common difference which is -3 and it is an arithmetic sequence.
Then let's find the nth term of the given sequence by using the formula for an arithmetic sequence:
An = A1 + (n - 1)d
where
An is the nth term,
A1 is the first term,
n is the number of terms, and
d is the common difference.
Let's substitute the given values to the formula.
An = A32
A1 = 4
n = 32
d = -3
A32 = 4 + (32 - 1)(-3)
A32 = 4 + (31)(-3)
A32 = 4 - 93
A32 = -89
Therefore, the 32nd term is -89.
