Final answer:
The nᵗʰ term of the sequence 18, 48, 78, 108, 138 is found using the arithmetic sequence formula, resulting in 30n - 12.
Step-by-step explanation:
To determine the nᵗʰ term of the sequence 18, 48, 78, 108, 138, we first need to identify the pattern in the sequence. By observing the differences between consecutive terms, we notice that each term is 30 more than the previous one; this means the sequence is arithmetic.
Since the first term, a₁, is 18, and the common difference, d, is 30, we can use the formula for the nᵗʰ term of an arithmetic sequence, which is aₙ = a₁ + (n - 1)d. Plugging the values in, we get aₙ = 18 + (n - 1)30. To simplify, aₙ = 18 + 30n - 30, which simplifies further to aₙ = 30n - 12. Therefore, the nᵗʰ term of the sequence is 30n - 12.
nth term = first term + (n-1) * common difference
Where the first term is 18 and the common difference is 30. Substituting these values in, we get:
nth term = 18 + (n-1) * 30