Final answer:
The nᵗʰ term of the arithmetic sequence 2, -88, -178, -268, -358 is given by the formula 92 - 90n.
Step-by-step explanation:
To determine the nᵗʰ term of a given sequence, we need to find a pattern that can represent any term in the sequence based on its position, denoted as n. The sequence provided is 2, -88, -178, -268, -358. We notice that from one term to the next, we are subtracting 90. Thus, the sequence appears to be an arithmetic sequence with a common difference of -90. The first term a1 is 2.
To find the nᵗʰ term of an arithmetic sequence, we use the formula:
an = a1 + (n - 1) * d,
where:
- an is the nᵗʰ term,
- a1 is the first term,
- n is the term number,
- d is the common difference.
Applying the formula to our sequence:
an = 2 + (n - 1) * (-90)
= 2 - 90n + 90
= 92 - 90n
Therefore, the nᵗʰ term of this sequence is 92 - 90n.