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So the only way to resolve this is to assume the sequence is symmetric around the center, i.e., $a - 2d, a - d, a, a + d, a + 2d$

First + Fifth = $2a = 14 \Rightarrow a = 7$

Therefore, the only consistent assumption is that the sequence is symmetric: $a - 2d, a - d, a, a + d, a + 2d$

Second + Fourth = $2a = 10 \Rightarrow a = 5$

Contradiction again. So the only way this works is if the sequence is not symmetric.

So again, contradiction.

So the only way to resolve this is to define theQuestion: A chemical engineer models the concentration of a reactant in a reactor over time with the function $ C(t) = rac{3t + 2}{t^2 + 4} $. For what values of $ t $ is the concentration increasing?

Solution: To determine when the concentration is increasing, we analyze the derivative of $ C(t) $. Using the quotient rule:

C'(t) = rac{(3)(t^2 + 4) - (3t + 2)(2t)}{(t^2 + 4)^2}

3(t^2 + 4) - 2t(3t + 2) = 3t^2 + 12 - (6t^2 + 4t) = -3t^2 - 4t + 12

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