if 1 is 5, 2 is 8, 3 is 11 and 4 is 14. What is n?

This appears to be a pattern where each value increases by 3 as the input increases by 1. Let's analyze this:

- When \( 1 \rightarrow 5 \)
- When \( 2 \rightarrow 8 \)
- When \( 3 \rightarrow 11 \)
- When \( 4 \rightarrow 14 \)

We can observe that each output is increasing by 3 compared to the previous one, which suggests a linear relationship between the input \( n \) and the output \( f(n) \).

We can describe this relationship as a linear equation:

\[
f(n) = 3n + 2
\]

### Derivation:
- For \( n = 1 \), \( f(1) = 3(1) + 2 = 5 \)
- For \( n = 2 \), \( f(2) = 3(2) + 2 = 8 \)
- For \( n = 3 \), \( f(3) = 3(3) + 2 = 11 \)
- For \( n = 4 \), \( f(4) = 3(4) + 2 = 14 \)

Thus, for any \( n \), the corresponding value is given by \( f(n) = 3n + 2 \).

If you have a specific value of \( n \) in mind, you can plug it into this equation to find the answer.

Would you like more details, or do you have any questions?

### Related Questions:
1. What would be the value when \( n = 10 \)?
2. How do you derive a general formula from a pattern of numbers?
3. What is the difference between a linear and a quadratic pattern?
4. How would the equation change if the pattern increased by 4 instead of 3?
5. Can you identify other types of number sequences, like geometric progressions?

**Tip**: Always look for differences between consecutive terms to identify a pattern type. Linear patterns have constant differences.

Discover how to find the linear equation for the pattern where 1 corresponds to 5, 2 corresponds to 8, and each subsequent value increases by 3. Learn how to derive the formula f(n) = 3n + 2 and apply it to find values of n. Suitable for students in Grades 6-8.

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