Final answer:
The sum of the 6th to the 20th terms of an arithmetic sequence with a first term of 11 and a common difference of 2 is 525.
Step-by-step explanation:
To find the sum of the 6th term to the 20th term with the first term of 11 and a common difference of 2, we first need to find the actual 6th and 20th terms using the formula for the nth term of an arithmetic sequence: Tn = a + (n - 1)d, where Tn is the nth term, a is the first term, and d is the common difference.
First, we calculate the 6th term (T6):
T6 = 11 + (6 - 1)(2) = 11 + 10 = 21.
Then, we calculate the 20th term (T20):
T20 = 11 + (20 - 1)(2) = 11 + 38 = 49.
Now, to find the sum of the terms from the 6th to the 20th, we'll use the formula for the sum of an arithmetic series: S = n/2 * (first term + last term), where n is the number of terms. Since we're starting from the 6th term and ending at the 20th term, there are 15 terms in total (20 - 6 + 1 = 15).
The sum from the 6th term to the 20th term is:
S = 15/2 * (21 + 49) = 7.5 * 70 = 525.