Final answer:
The sequence is arithmetic with a first term of 3 and a common difference of 3.9. The formula for the nᵗʰ term is aₙ = 3 + (n - 1)3.9, and this can be used to calculate any term in the sequence.
Step-by-step explanation:
To determine the nᵗʰ term of the given sequence, let's take a look at the patterns and differences between the terms. Starting with the sequence 3, 6.9, 10.8, 14.7, 18.6, we observe that the difference between consecutive terms increases by a fixed amount, which indicates that this could be an arithmetic sequence. The common difference in this case is the second term minus the first term, which is 6.9 - 3 = 3.9. Applying this difference sequentially to the next terms, we confirm that each term indeed increases by 3.9 from the preceding term.
The formula for the nᵗʰ term of an arithmetic sequence is given by aᵢ = a₁ + (i - 1)d, where a₁ is the first term and d is the common difference. So, for our sequence, a₁ = 3 and d = 3.9. Therefore, the nᵗʰ term of the sequence is aₙ = 3 + (n - 1)3.9.
To summarize, we can use this formula to find any term within the sequence. For example, the 10th term would be calculated by substituting n = 10 into the formula: a₁₀ = 3 + (10 - 1)3.9 = 3 + 9 x 3.9 = 3 + 35.1 = 38.1.