Final answer:
The sum of the first 15 terms of the arithmetic sequence is 135.
Step-by-step explanation:
An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant.
The given arithmetic sequence is un = 41 - 4n.
To find the sum of the first 15 terms, we can use the formula for the sum of an arithmetic series:
Sn = (n/2)(a1 + an), where Sn is the sum of the first n terms, a1 is the first term, and an is the last term.
In this case, n = 15, a1 = u1 = 41 - 4(1) = 37, and an = u15 = 41 - 4(15) = -19.
Substituting these values into the formula, we get:
S15 = (15/2)(37 + (-19)) = (15/2)(18) = 135.
Therefore, the sum of the first 15 terms of the arithmetic sequence is 135.