Let's find the first three terms for each of the sequences given:

1. Sequence $a_n = 3n - 5$

For the first three terms, plug in $n = 1, 2, 3$ into the formula:

• $a_1 = 3(1) - 5 = 3 - 5 = -2$
• $a_2 = 3(2) - 5 = 6 - 5 = 1$
• $a_3 = 3(3) - 5 = 9 - 5 = 4$

So, the first three terms are: $-2, 1, 4$

2. Sequence $a_n = n(n + 1)$

Again, for the first three terms, plug in $n = 1, 2, 3$:

• $a_1 = 1(1 + 1) = 1 \times 2 = 2$
• $a_2 = 2(2 + 1) = 2 \times 3 = 6$
• $a_3 = 3(3 + 1) = 3 \times 4 = 12$

So, the first three terms are: $2, 6, 12$

3. Sequence defined by $2n = 2^n - 3$

Here, you need to solve the equation for $n$ to find each term $a_n$. The sequence is defined implicitly:

• For $n = 1$: $2(1) = 2^1 - 3 \Rightarrow 2 = 2 - 3$ (not true)
• For $n = 2$: $2(2) = 2^2 - 3 \Rightarrow 4 = 4 - 3 = 1$ (not true)
• For $n = 3$: $2(3) = 2^3 - 3 \Rightarrow 6 = 8 - 3 = 5$ (not true)

It appears the equation $2n = 2^n - 3$ does not produce a valid sequence for the first few values of $n$. This is a non-standard sequence, and might have no solutions for small $n$.

Therefore, the first two sequences produce valid terms:

1. $-2, 1, 4$
2. $2, 6, 12$

The third sequence requires a different approach or clarification.

Would you like further details on any of these?

Here are five related questions you might consider:

1. What happens if we try a different formula for the third sequence?
2. How can we derive a formula if given a non-standard sequence?
3. Can we find a recursive definition for the first or second sequences?
4. What would be the first three terms if the formula in sequence 1 was modified?
5. How does the pattern change if we alter the starting index $n$ for these sequences?

Tip: When working with sequences, always ensure that the formula works for all given values of $n$ before assuming it's a standard sequence.