Final answer:
The nᵗʰ term of the sequence 12, 21, 30, 39, 48 can be found using the arithmetic sequence formula. The formula is an = 9n + 3, where n represents the term number in the sequence.
Step-by-step explanation:
The sequence given is 12, 21, 30, 39, 48, and the pattern suggests that each term increases by 9 from the previous term. To find the nᵗʰ term of the sequence, we can use the formula for an arithmetic sequence, which is an = a1 + (n - 1)d, where a1 is the first term and d is the common difference between the terms.
In this case, a1 is 12 and d is 9. Plugging these values into the formula gives us an = 12 + (n - 1) × 9. Simplifying this expression, we get an = 9n + 3, which is the formula for the nᵗʰ term of the given sequence.
The given sequence is 12, 21, 30, 39, 48. To determine its nᵗʰ term, we can observe a pattern. The difference between each term in the sequence is 9. So, the sequence can be represented by the equation:
aₙ = a₁ + (n - 1)d
where aₙ is the nᵗʰ term, a₁ is the first term, n is the position of the term, and d is the common difference.
Plugging in the values, we have:
aₙ = 12 + (n - 1)(9)
Therefore, the nᵗʰ term of the sequence 12, 21, 30, 39, 48 is 12 + (n - 1)(9).