Find the nth Term Formula for Sequence: 7, 11, 15, 19, 23

Given the series whose difference between two jumped numbers is constant:

$7,11,15,19,23$

Describe the property using the variable $n$

To solve this problem, we'll follow these steps:

• Step 1: Identify the first term and the common difference.
• Step 2: Use the arithmetic sequence formula to express the series.
• Step 3: Construct the formula based on the calculations.

Now, let's work through each step:
Step 1: The first term $a_1$ of the series is $7$. Calculate the common difference $d$ as the difference between two consecutive terms. Between $7$ and $11$, the difference is $4$, and this holds for each consecutive pair of terms. Thus, $d = 4$.

Step 2: We'll use the formula for the $n$-th term of an arithmetic sequence, which is $a(n) = a_1 + (n-1) \times d$.

Step 3: Substitute the values for $a_1$ and $d$ into the formula:
$a(n) = 7 + (n-1) \times 4$.

Therefore, the solution to the problem is $a(n)=7+(n-1)\times4$.