Worksheet on forming algebraic expressions for numbers, sequences, sums, and products.

To solve this problem, we need to translate words into algebra using the variable $n$, which represents any integer (whole number like 1, 2, -5, etc.).

Here is the step-by-step logic for each row:

1. A number: The problem states that $n$ is any integer. So, we simply use $n$.
2. An even number: Even numbers are multiples of 2 (like 2, 4, 6). To represent any even number, we multiply our integer by 2. Expression: $2n$.
3. An odd number: Odd numbers are always 1 more or 1 less than an even number. Since $2n$ is even, adding 1 makes it odd. Expression: $2n + 1$ (or $2n - 1$).
4. Two consecutive numbers: "Consecutive" means following one after another (like 5 and 6). If the first number is $n$, the next one is just $n + 1$. Expressions: $n, n + 1$.
5. Two consecutive even numbers: Even numbers are 2 apart (like 4 and 6). If the first even number is $2n$, the next one is $2n + 2$. Expressions: $2n, 2n + 2$.
6. Two consecutive odd numbers: Odd numbers are also 2 apart (like 3 and 5). If the first odd number is $2n + 1$, the next one is $(2n + 1) + 2$, which simplifies to $2n + 3$. Expressions: $2n + 1, 2n + 3$.
7. The sum of two consecutive numbers: We take the two numbers from step 4 ($n$ and $n + 1$) and add them together.
Calculation: $n + (n + 1) = 2n + 1$. Expression: $2n + 1$.

Final Answer:

| Forming Expressions | Algebraic Expression |
| :--- | :--- |
| A number | $n$ |
| An even number | $2n$ |
| An odd number | $2n + 1$ |
| Two consecutive numbers | $n, n + 1$ |
| Two consecutive even numbers | $2n, 2n + 2$ |
| Two consecutive odd numbers | $2n + 1, 2n + 3$ |
| The sum of two consecutive numbers | $2n + 1$ |