Final answer:
To find the first term of the arithmetic sequence, we first calculate the common difference and then use it to determine the first term. Subtracting 17 times the common difference from the 18th term, we find that the first term is -286.
Step-by-step explanation:
To find the first term of an arithmetic sequence given the 18th and 20th terms, we can use the formula for any term in an arithmetic sequence: a_n = a_1 + (n - 1) * d, where a_n is the nth term, a_1 is the first term, and d is the common difference. We are given that the 18th term (a_18) is 20 and the 20th term (a_20) is 56. First, we find the common difference (d) by subtracting the 18th term from the 20th term and dividing by the difference in their positions:
d = (a_20 - a_18) / (20 - 18) = (56 - 20) / 2 = 18
Now we have the common difference, we can solve for the first term using the 18th term:
a_1 = a_18 - (18 - 1) * d = 20 - 17 * 18
By computing this, we get:
a_1 = 20 - 306 = -286
Therefore, the first term of the arithmetic sequence is -286.