The sequence provided is: 15, 13, 11, ...

To find the formula for the $n$-th term, we start by identifying the pattern. Let's observe the differences between consecutive terms:

• $13 - 15 = -2$
• $11 - 13 = -2$

The sequence is decreasing by 2 each time. This tells us that it is an arithmetic sequence with a common difference of $d = -2$.

General Formula for an Arithmetic Sequence

The formula for the $n$-th term of an arithmetic sequence is given by:

$a_n = a_1 + (n - 1) \cdot d$

Where:

• $a_n$ is the $n$-th term.
• $a_1$ is the first term of the sequence.
• $n$ is the term number.
• $d$ is the common difference.

Plugging in the Values

For this sequence:

• $a_1 = 15$
• $d = -2$

Thus, the $n$-th term formula becomes:

$a_n = 15 + (n - 1) \cdot (-2)$

Simplifying:

$a_n = 15 - 2(n - 1)$ $a_n = 17 - 2n$

Final Answer

The formula for the $n$-th term of the sequence is:

$a_n = 17 - 2n$

Would you like to see more details or have any questions?

Related Questions:

1. What is the value of the 10th term using the formula $a_n = 17 - 2n$?
2. How would the formula change if the sequence started from 20 instead of 15?
3. Can you derive a formula for a similar sequence with a common difference of -3?
4. What is the sum of the first 5 terms of the sequence?
5. How do you find the general formula for a geometric sequence?

Tip:

For arithmetic sequences, always check the common difference between terms. If the difference is constant, use the standard formula $a_n = a_1 + (n - 1) \cdot d$.