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.