Final answer:
To find the nᵗʰ term of the arithmetic sequence, calculate the common difference using the given terms and then use the formula for the nᵗʰ term of an arithmetic sequence. The nᵗʰ term is found to be 2n + 7.
Step-by-step explanation:
The student is asked to determine the nᵗʰ term of an arithmetic sequence when the third term is 11 and the fifth term is 15. An arithmetic sequence has a common difference (d), which can be calculated by subtracting the third term from the fifth term and then dividing by the number of terms between them. In this case:
5th term - 3rd term = 15 - 11 = 4
The number of terms between the 3rd and 5th terms is 2 (because 5 - 3 = 2)
So, the common difference (d) is 4 / 2 = 2.
Once we have the common difference, we can calculate the first term (a1) by subtracting two times the common difference from the third term:
a1 = 11 - (2 - 1) * 2 = 11 - 2 = 9
The nᵗʰ term of an arithmetic sequence is given by the formula:
aₙ = a₁ + (n - 1) * d
Therefore, the nᵗʰ term can be expressed as:
aₙ = 9 + (n - 1) * 2
Simplifying that:
aₙ = 9 + 2n - 2
aₙ = 2n + 7
The nᵗʰ term of the given arithmetic sequence is 2n + 7.