1. The problem is to find the sum of an arithmetic progression (AP) using the arithmetic progression method. 2. The formula for the sum of the first $n$ terms of an AP is $$S_n = \frac{n}{2} (2a + (n-1)d)$$ where $a$ is the first term, $d$ is the common difference, and $n$ is the number of terms. 3. Important rules: - The terms increase or decrease by a constant difference $d$. - The sum formula works for any number of terms $n$. 4. To use the method, identify $a$, $d$, and $n$ from the problem. 5. Substitute these values into the formula and simplify step-by-step. 6. For example, if $a=3$, $d=2$, and $n=5$, then: $$S_5 = \frac{5}{2} (2\times3 + (5-1)\times2) = \frac{5}{2} (6 + 8) = \frac{5}{2} \times 14 = 35$$ 7. Thus, the sum of the first 5 terms is 35. This method efficiently calculates the sum of an arithmetic progression.