The 9th term in a sequence is 16.  If the common difference is 2, find the 1st term.

The given problem relates to an arithmetic sequence, where the \(n\)-th term of the sequence can be expressed as:  

\[
a_n = a + (n-1)d
\]

Where:  
- \(a\) is the first term,  
- \(d\) is the common difference,  
- \(n\) is the term number,  
- \(a_n\) is the \(n\)-th term.

### Given:
- \(a_9 = 16\),
- \(d = 2\),
- \(n = 9\).

Substitute into the formula:

\[
16 = a + (9-1)(2)
\]

Simplify:

\[
16 = a + 16
\]

Solve for \(a\):

\[
a = 16 - 16 = 0
\]

### Solution:
The first term of the sequence (\(a\)) is **0**.  

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Would you like further explanation or examples?  

### Related Questions:
1. What is the general formula for finding the \(n\)-th term of an arithmetic sequence?
2. How do you find the sum of the first \(n\) terms in an arithmetic sequence?
3. If the 12th term of the same sequence is given, how would you verify the first term?
4. What happens if the common difference changes to a different value?
5. How do you identify whether a sequence is arithmetic or geometric?

### Tip:
Always double-check your substitution into the formula to ensure accuracy when solving arithmetic sequence problems.

The 9th term in a sequence is 16. If the common difference is 2, find the 1st term.

Learn how to calculate the first term of an arithmetic sequence where the 9th term is 16 and the common difference is 2. This problem involves the arithmetic sequence formula and is suitable for Grades 6-8.

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