Final answer:
To find the nth term of an arithmetic sequence, we first find the common difference (d) by subtracting the third term from the fifth term. Then, we use the formula an = a1 + (n-1)d, where an is the nth term, a1 is the first term, n is the term number, and d is the common difference, to find the nth term of the sequence. In this case, the nth term is 16n - 17.
Step-by-step explanation:
To find the nth term of an arithmetic sequence, we need to first find the common difference (d) between consecutive terms. In this case, we can find d by subtracting the third term (31) from the fifth term (47), which gives us d = 47 - 31 = 16. Once we have the common difference, we can use the formula for the nth term of an arithmetic sequence:
an = a1 + (n-1)d
where an is the nth term, a1 is the first term, n is the term number, and d is the common difference. In this case, we know that the third term (a3) is 31, so we can substitute those values into the formula and solve for an:
a3 = a1 + (3-1)d = 31
a1 + 2d = 31
a1 + 32 = 31
a1 = 31 - 32 = -1
Now, we can substitute the values of a1, n, and d back into the formula to find the nth term:
an = -1 + (n-1)(16)
So the nth term of the sequence is -1 + 16n - 16 = 16n - 17.