Question

Complete a general function for the sequence: 5/2,6/2,7/2,8/2,9/2,…



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Answer 1

To find a general function for the sequence \( a_n = \frac{5}{2}, \frac{6}{2}, \frac{7}{2}, \frac{8}{2}, \frac{9}{2}, \ldots \), we first observe the pattern in the numerators:

- The numerator starts at 5 and increases by 1 for each subsequent term.

So the numerators are:
- For \( n=1 \): \( 5 \)
- For \( n=2 \): \( 6 \)
- For \( n=3 \): \( 7 \)
- For \( n=4 \): \( 8 \)
- For \( n=5 \): \( 9 \)

We can see that the numerator can be described by the formula \( 4 + n \) (since \( 4 + 1 = 5 \), \( 4 + 2 = 6 \), ..., \( 4 + 5 = 9 \)).

Therefore, we can express the nth term of the sequence as:
\[
a_n = \frac{4 + n}{2}
\]

Thus, the general function for the sequence is:
\[
a_n = \frac{4 + n}{2}
\]