Final answer:
To determine the nᵗʰ term of the given sequence, we found the common difference and used the formula for an arithmetic sequence. The nᵗʰ term is 90n - 77.
Step-by-step explanation:
The given sequence is 13, 103, 193, 283, 373. To find the nᵗʰ term of this arithmetic sequence, we must first identify the common difference. The difference between consecutive terms is 90 (103 - 13 = 90, 193 - 103 = 90, and so on).
Knowing that an arithmetic sequence follows the pattern a_n = a_1 + (n - 1)d where a_n is the nᵗʰ term, a_1 is the first term, n is the term number, and d is the common difference, we can plug in our values:
a_n = 13 + (n - 1) × 90
Expanding this, we get:
a_n = 13 + 90n - 90
a_n = 90n - 77
Therefore, the nᵗʰ term of this sequence is 90n - 77.