An arithmetic sequence is given by the following formula:
an = a1 + d(n - 1)
Where a1 is the first term and d is the common difference. In this case, we are given the values of a11 and a15, then we can formulate the following expressions:
a11 = a1 + d(11 - 1)
a11 = a1 + d(10)
a11 = a1 + 10d
26 = a1 + 10d
Similarly for a15:
a15 = a1 + d(15 - 1)
a15 = a1 + 14d
-10 = a1 + 14d
Then, we got two equations:
26 = a1 + 10d
-10 = a1 + 14d
By subtracting the first from the second one, we get:
-10 - 26 = a1 - a1 + 14d - 10d
-36 = 4d
From this equation, we can solve for d by dividing both sides by 4, like this:
-36/4 = 4d/4
-9 = d
d = -9
Now that we know the value of d, we can replace it into 26 = a1 + 10d to find a1, like this:
26 = a1 + 10(-9)
26 = a1 - 90
26 + 90 = a1 - 90 + 90
116 = a1 + 0
a1 = 116
Then, a1 = 116 and we can rewrite the model like this:
an = 116 - 9(n-1)
By replacing 28 for n we get the value of a28:
a28 = 116 - 9(28 - 1)
a28 = 116 - 9(27)
a28 = 116 - 243
a28 = -127
Then, a28 = -127, the third option is the correct answer