Final answer:
The given sequence is arithmetic with a common difference of -160. Using the first term and common difference, we can find the nᵗʰ term of the sequence, which is 178 - 160n.
Step-by-step explanation:
The sequence given is 18, -142, -302, -462, -622. To determine the nth term of this sequence, we need to identify the pattern or rule that defines the sequence.
Firstly, let's look at the differences between successive terms:
- -142 - 18 = -160
- -302 - (-142) = -160
- -462 - (-302) = -160
- -622 - (-462) = -160
So, the difference between consecutive terms is consistent at -160. This means the sequence is arithmetic with a common difference of -160.
If the first term (a1) is 18 and the common difference (d) is -160, we can use the nth term formula for an arithmetic sequence:
an = a1 + (n - 1) * d
Plugging in the values, we get:
an = 18 + (n - 1) * (-160) = 18 - 160n + 160 = 178 - 160n
Hence, the nth term of the given sequence is 178 - 160n.