Final answer:
To find the sum of the first 20 terms of an arithmetic series, we need to find the common difference and the first term of the series using the given information. Then, we can use the formula for the sum of an arithmetic series to calculate the sum.
Step-by-step explanation:
To find the sum of the first 20 terms of an arithmetic series given the fourth term and the twelfth term, we need to first find the common difference and the first term of the series.
Using the formula for the nth term of an arithmetic series, we can set up two equations using the given information:
4th term: a + 3d = 22 12th term: a + 11d = 54
Solving these equations simultaneously, we can find the values of the first term (a) and the common difference (d). Once we have these values, we can use the formula for the sum of an arithmetic series to find the sum of the first 20 terms.