The sequence $a_n = (-1)^n 17n^2$ can be computed term by term using the given formula:

1. First term ($n = 1$): $a_1 = (-1)^1 \cdot 17 \cdot 1^2 = -17$

2. Second term ($n = 2$): $a_2 = (-1)^2 \cdot 17 \cdot 2^2 = 1 \cdot 17 \cdot 4 = 68$

3. Third term ($n = 3$): $a_3 = (-1)^3 \cdot 17 \cdot 3^2 = -1 \cdot 17 \cdot 9 = -153$

4. Fourth term ($n = 4$): $a_4 = (-1)^4 \cdot 17 \cdot 4^2 = 1 \cdot 17 \cdot 16 = 272$

5. 100th term ($n = 100$): $a_{100} = (-1)^{100} \cdot 17 \cdot 100^2 = 1 \cdot 17 \cdot 10000 = 170000$

Final Results:

• First term: $-17$
• Second term: $68$
• Third term: $-153$
• Fourth term: $272$
• 100th term: $170000$

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Would you like a detailed explanation of the alternating sign behavior or the calculations? Here are some follow-up questions:

1. How does the term $(-1)^n$ affect the sequence behavior?
2. What happens to the sequence as $n$ becomes very large?
3. How could you generalize the absolute growth of this sequence?
4. What is the sum of the first four terms of the sequence?
5. How would the sequence change if $n^3$ replaced $n^2$?

Tip: The term $(-1)^n$ is responsible for alternating the sign of the sequence. Odd values of $n$ produce negative terms, while even values produce positive terms.