Final answer:
The nᵗʰ term of the arithmetic sequence 17, 27, 37, 47, 57 is found using the formula Tₙ = a₁ + (n - 1)d, which gives us the nᵗʰ term as 10n + 7.
Step-by-step explanation:
To determine the nᵗʰ term of the given sequence 17, 27, 37, 47, 57, we can see that the sequence is arithmetic, meaning it has a common difference between consecutive terms. The first term, a₁, is 17 and the common difference, d, is 27 - 17 = 10. To find the nᵗʰ term, use the formula for the nᵗʰ term of an arithmetic sequence:
Tₙ = a₁ + (n - 1)d
Substitute the known values into the equation:
Tₙ = 17 + (n - 1) * 10
Solving for Tₙ gives us:
Tₙ = 17 + 10n - 10
Tₙ = 10n + 7
Therefore, the nᵗʰ term of the sequence is 10n + 7.