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The given sequence has the general term:

\[
a_n = 51 + 3(n - 10)
\]

We are tasked with finding which of the provided expressions also gives the general term of the sequence.

Let's first simplify the expression for \( a_n \):

\[
a_n = 51 + 3(n - 10)
\]

Distribute the \( 3 \):

\[
a_n = 51 + 3n - 30
\]

Now combine like terms:

\[
a_n = 3n + 21
\]

So, the simplified general term is \( a_n = 3n + 21 \).

Looking at the options:

- **A:** \( 10 + 3(51 - n) \) — Not equivalent to the simplified form.
- **B:** \( 17 + 3n \) — Not equivalent.
- **C:** \( 21 + 3n \) — This matches the simplified form.
- **D:** \( 51 \cdot 3^{(n - 10)} \) — Not equivalent to the simplified form.

The correct answer is **C**.

Would you like further details, or do you have any other questions?

Here are 5 related questions for further practice:
1. How do you identify arithmetic sequences from general terms?
2. What is the general form of an arithmetic sequence?
3. How do you simplify expressions involving distribution?
4. How do constants affect the progression of a sequence?
5. How can you check if a term is linear or nonlinear?

**Tip:** Simplifying a sequence's general term often involves distributing coefficients and combining like terms. Always simplify before comparing to other forms.

The general term of a sequence is given by a_n = 51 + 3(n - 10), where a_0 is the initial value. Which of the following expressions also gives the general term of the sequence?

Learn how to simplify the general term of a sequence given by a_n = 51 + 3(n - 10). This problem involves algebraic manipulation and understanding arithmetic sequences. Suitable for students in Grades 8-10.

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