Final answer:
The sequence provided is arithmetic, with a common difference of 6. The nᵗʰ term can be calculated using the formula Tn = 15 + (n - 1)6, which simplifies to Tn = 6n + 9, representing the nᵗʰ term of the sequence.
Step-by-step explanation:
The given sequence is 15, 21, 27, 33, 39. This sequence shows a common difference between consecutive terms, which is a characteristic of an arithmetic sequence. By subtracting any term from the subsequent term, we find the common difference; 21 - 15 = 6. Thus, the sequence increases by 6 each time. To find the nᵗʰ term of an arithmetic sequence, we use the formula Tn = a + (n - 1)d, where Tn is the nᵗʰ term, a is the first term, n is the term number, and d is the common difference.
For this sequence:
a = 15 (the first term),
d = 6 (the common difference).
Therefore, the nᵗʰ term is given by:
Tn = 15 + (n - 1)6.
Expanding this equation, we get:
Tn = 15 + 6n - 6,
which simplifies to
Tn = 6n + 9.
The nᵗʰ term of the sequence is therefore 6n + 9.