Final answer:
The nᵗʰ term of the given sequence is found using the arithmetic sequence formula aₙ = a₁ + (n - 1)d. With a common difference of 33 and the first term being -9, the nᵗʰ term is aₙ = 33n - 42.
Step-by-step explanation:
The student is asking for the nᵗʰ term of the sequence -9, 24, 57, 90, 123. To find the nᵗʰ term of a sequence, it's often useful to look at the differences between terms to see if there is a consistent pattern or to find a function that describes the sequence.
Let's find the differences between successive terms: 24 - (-9) = 33, 57 - 24 = 33, 90 - 57 = 33, and 123 - 90 = 33. Since each term increases by 33, we can conclude that the sequence is arithmetic with a common difference of 33. The first term, -9, is the value when n=1.
To find the nᵗʰ term (aₙ) of an arithmetic sequence, we use the formula aₙ = a₁ + (n - 1)d, where a₁ is the first term and d is the common difference. Substituting our values, we get aₙ = -9 + (n - 1)*33. Simplifying, the expression for the nᵗʰ term is aₙ = 33n - 42.
The given sequence is -9, 24, 57, 90, 123. To determine its nᵗʰ term, we need to find a pattern in the sequence.
By observing the sequence, we can see that the common difference between consecutive terms is 33.
The formula for the nth term of an arithmetic sequence is a + (n - 1)d, where a is the first term and d is the common difference. In this case, a = -9 and d = 33.
So, the nth term of the sequence is -9 + (n - 1)33.