The sum of the second and sixth terms of an arithmetic sequence is 4.
The third term is 24 more than the 11th term.
Let's denote the common difference of the arithmetic sequence as d.
The second term is given by: a + d
The sixth term is given by: a + 5d
The eleventh term is given by: a + 10d
From the given information, we can create the following equations:
a + d + a + 5d = 4
2a + 6d = 4
a + 3d = 2
Also, we are given that the third term is 24 more than the eleventh term:
a + 2d = a + 10d + 24
- 8d = 24
d = -3
Substitute d = -3 into the equation a + 3d = 2:
a + 3(-3) = 2
a - 9 = 2
a = 11
Therefore, the arithmetic sequence is 11, 8, 5, 2, -1, -4, ...