The given sequence is $7, 11, 15, \dots$.

Step 1: Identify the pattern

The sequence appears to be an arithmetic progression (AP) because the difference between consecutive terms is constant:

$11 - 7 = 4 \quad \text{and} \quad 15 - 11 = 4.$

Thus, the common difference $d = 4$.

Step 2: General formula for the nth term

For an arithmetic sequence, the nth term is given by the formula:

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

where:

• $a_n$ is the nth term,
• $a_1$ is the first term (7),
• $d$ is the common difference (4),
• $n$ is the term number.

Step 3: Find the 10th term ($a_{10}$)

Now, using the formula, we can find $a_{10}$:

$a_{10} = 7 + (10-1) \cdot 4$ $a_{10} = 7 + 9 \cdot 4 = 7 + 36 = 43.$

Thus, $a_{10} = 43$.

Final Answer:

• The general formula for the nth term is:
  $a_n = 7 + (n-1) \cdot 4.$

• The 10th term $a_{10}$ is $43$.

Would you like more details on arithmetic sequences, or do you have any questions?

Here are some related questions:

1. What is the sum of the first 10 terms of this sequence?
2. How can we prove that this sequence is arithmetic?
3. What is the 20th term of this sequence?
4. What is the difference between an arithmetic and a geometric sequence?
5. How would the sequence change if the common difference were -4?

Tip: In any arithmetic sequence, the nth term can be quickly calculated using the formula $a_n = a_1 + (n-1) \cdot d$, where $a_1$ is the first term and $d$ is the common difference.