Final answer:
The formula for the nth term of the arithmetic sequence is an = 43 + (n - 1) × 2, based on the 20th term being 81 and a common difference of 2.
Step-by-step explanation:
To find the formula for the nth term of an arithmetic sequence when you know the 20th term and the common difference, you first need to 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, d is the common difference, and n is the term number. Given the 20th term (a20) is 81 and common difference (d) is 2, we can substitute into the formula to find a1.
81 = a1 + (20 - 1) × 2
a1 = 81 - 38
a1 = 43
Now that we have the first term, the general formula for the nth term of the sequence can be written as:
an = 43 + (n - 1) × 2