It looks like you provided a sequence of numbers: 1, 2, 3, 4, 5, 6. This sequence is an arithmetic sequence where the difference between each consecutive number is 1.

Basic Properties of the Sequence:

• First Term (a₁): 1
• Common Difference (d): 1 (since 2 - 1 = 1, 3 - 2 = 1, etc.)
• Number of Terms (n): 6
• Sum of the Sequence (Sₙ): The sum of an arithmetic sequence can be calculated using the formula: $Sₙ = \frac{n}{2} \times (a₁ + aₙ)$ where $a₁$ is the first term and $aₙ$ is the last term.

Let me calculate the sum of this sequence.

The sum of the sequence $1, 2, 3, 4, 5, 6$ is 21.

Would you like more details on how the arithmetic sequence formula works, or do you have any specific questions?

Here are five related questions that expand on this topic:

1. What is the formula for finding the $n$th term of an arithmetic sequence?
2. How do you find the common difference in an arithmetic sequence?
3. What are some examples of arithmetic sequences with different common differences?
4. How do you calculate the sum of an arithmetic sequence when the number of terms is unknown?
5. Can you apply arithmetic sequence concepts to solve real-world problems, such as calculating savings?

Tip: In arithmetic sequences, the sum can be calculated efficiently using the formula $S_n = \frac{n}{2} \times (a_1 + a_n)$, which works regardless of how large $n$ is.