Final answer:
To find the sum of the first 20 terms of an arithmetic series, use the formulas for the nth term and the sum of an arithmetic series.
Step-by-step explanation:
To find the sum of the first 20 terms of an arithmetic series, we need to know the formula for the nth term of an arithmetic sequence. The formula is: an = a1 + (n-1)d, where an is the nth term, a1 is the first term, and d is the common difference.
Given that the fourth term is 21 and the 12th term is 44, we can write two equations:
21 = a1 + 3d (equation 1)
44 = a1 + 11d (equation 2)
Solving these equations simultaneously, we can find the values of a1 and d. Once we have these values, we can use the formula for the sum of an arithmetic series: Sn = (n/2)(2a1 + (n-1)d), where Sn is the sum of the first 'n' terms.