Final answer:
The nth term of the arithmetic sequence with a first term of 17 and a second term of 47 is found using the formula for the nth term of an arithmetic sequence. The common difference (d) is 30, leading to the formula 30n - 13 for the nth term.
Step-by-step explanation:
To determine the nth term of the arithmetic sequence where the first term is 17 and the second term is 47, we first need to find the common difference (d) of the sequence. The common difference is obtained by subtracting the first term from the second term: d = 47 - 17 = 30.
Now, the nth term of an arithmetic sequence can be found using the formula: nth term = a + (n - 1)d, where 'a' is the first term and 'd' is the common difference. For this sequence, a = 17 and d = 30. Plugging in these values, we get:
nth term = 17 + (n - 1)×30
To express this in a simplified form, distribute the 30 and simplify: nth term = 17 + 30n - 30 = 30n - 13.
Therefore, the formula for the nth term of an arithmetic sequence starting with 17 and having a common difference of 30 is 30n - 13.