Let's solve this step by step:

Given

The formula for the nth term of the arithmetic sequence is: $u_n = 55 - 2n$

Part a) Write down the first 3 terms of the sequence.

For the first term ($n = 1$): $u_1 = 55 - 2(1) = 55 - 2 = 53$

For the second term ($n = 2$): $u_2 = 55 - 2(2) = 55 - 4 = 51$

For the third term ($n = 3$): $u_3 = 55 - 2(3) = 55 - 6 = 49$

So, the first 3 terms of the sequence are: $53, 51, 49$.

Part b) Find the first term in the sequence that is negative.

We need to find $n$ such that: $u_n = 55 - 2n < 0$

Solving this inequality: $55 - 2n < 0$ $55 < 2n$ $n > \frac{55}{2} = 27.5$

Since $n$ must be a whole number, the smallest $n$ for which the term is negative is $n = 28$.

For $n = 28$: $u_{28} = 55 - 2(28) = 55 - 56 = -1$

Thus, the first negative term occurs when $n = 28$, and that term is $-1$.

Would you like more details on any of these steps? Here are five related questions you might explore:

1. How do you find the general term of an arithmetic sequence from its first few terms?
2. What is the common difference in this sequence, and how does it affect the pattern of the terms?
3. Can you derive a formula for when the nth term of an arithmetic sequence will become zero or negative?
4. How would this sequence change if the formula were $u_n = 55 + 2n$ instead?
5. What is the sum of the first 28 terms of this sequence?

Tip: When analyzing arithmetic sequences, always identify the common difference, as it helps to predict the behavior of the sequence over time.