Find a function that describes the arithmetic sequence.

Question

11.5, 12.5, 13.5, 14.5,...
Use y to identify each term in the sequence and n to identify each term's position.

Answer 1

An arithmetic sequence can be described using the formula:

$$y_n=a+(n-1)d$$

where:

• $y_n$ is the $n$-th term in the sequence,
• $a$ is the first term,
• $d$ is the common difference,
• $n$ is the position of the term in the sequence.

For the given sequence $11.5,12.5,13.5,14.5,\dots$:

1. The first term $a=11.5$.
2. The common difference $d=12.5-11.5=1$.

Now we can substitute these values into the formula:

$$y_n=11.5+(n-1)\cdot 1$$

Simplifying this, we get:

$$y_n=11.5+n-1$$ $$y_n=n+10.5$$

Therefore, the function that describes the arithmetic sequence is:

$$y_n=n+10.5$$