To find the 61st term of the given arithmetic sequence, we first need to establish the key components of the sequence:

Sequence:

$3, 10, 17, 24, \dots$

Step 1: Determine the Common Difference ($d$)

The common difference $d$ in an arithmetic sequence is found by subtracting the first term from the second term: $d = 10 - 3 = 7$

Step 2: Use the Formula for the $n$-th Term of an Arithmetic Sequence

The formula to find the $n$-th term of an arithmetic sequence is: $a_n = a_1 + (n - 1) \cdot d$ where:

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

Step 3: Plug in the Values to Find the 61st Term

Here, we need to find the 61st term ($n = 61$). The first term $a_1 = 3$, and the common difference $d = 7$. Using the formula: $a_{61} = 3 + (61 - 1) \cdot 7$ $a_{61} = 3 + 60 \cdot 7$ $a_{61} = 3 + 420 = 423$

Final Answer:

The 61st term of the arithmetic sequence is 423.

Would you like further explanation or details on any step?

Here are some follow-up questions that build on this:

1. How do you find the sum of the first 61 terms of this sequence?
2. Can you generalize a formula to find any term in the sequence?
3. What would be the 100th term of this sequence?
4. How do arithmetic sequences differ from geometric sequences?
5. How can you determine whether a sequence is arithmetic?

Tip: The common difference $d$ is the key characteristic of an arithmetic sequence, making it easy to predict future terms using simple addition.