Final answer:
In an arithmetic sequence, the sum of the first six odd-numbered terms is given as 60, the sum of the first eleven terms is 836
Step-by-step explanation:
In an arithmetic sequence, the difference between consecutive terms is constant.
To find the sum of an arithmetic sequence, we use the formula Sn = (n/2)(a1 + an), where Sn is the sum of the first n terms, a1 is the first term, and an is the nth term.
Sum of the First Six Odd-Numbered Terms
The first term in an arithmetic sequence with odd numbers is a1 = 1, and the common difference is d = 2 (since the numbers increase by 2).
We are given the sum of the first six odd-numbered terms as 60. Plugging these values into the formula, we get:
S6 = (6/2)(1 + a6) = 60
(3)(1 + a6) = 60
1 + a6 = 20
a6 = 19
Sum of the First Eleven Terms
Using the same formula, we can find the sum of the first eleven terms:
S11 = (11/2)(1 + a11) = (11/2)(1 + 37) = 22 * 38 = 836
Therefore the sum of the first eleven terms is 836