1. What is the First Term of Arithmetic Progression Formula?

The formula calculates the first term of an arithmetic progression when the last term, total number of terms, and common difference are known. This is essential for reconstructing arithmetic sequences from partial information.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( a \) — First Term of Progression
• \( l \) — Last Term of Progression
• \( n_{Total} \) — Number of Total Terms of Progression
• \( d \) — Common Difference of Progression

Explanation: The formula works backwards from the last term by subtracting the accumulated differences to find the starting value of the arithmetic progression.

3. Importance of First Term Calculation

Details: Calculating the first term is crucial for understanding the complete arithmetic sequence, analyzing patterns, and solving problems in mathematics, physics, and engineering where arithmetic progressions are used.

4. Using the Calculator

Tips: Enter the last term of the progression, the total number of terms (must be at least 1), and the common difference between terms. All values must be valid numerical inputs.

5. Frequently Asked Questions (FAQ)

Q1: What is an arithmetic progression?
A: An arithmetic progression is a sequence of numbers where the difference between consecutive terms is constant.

Q2: Can this formula be used for any arithmetic sequence?
A: Yes, this formula works for any arithmetic progression where the last term, total terms, and common difference are known.

Q3: What if the common difference is negative?
A: The formula works equally well for negative common differences, resulting in a decreasing arithmetic progression.

Q4: How accurate is this calculation?
A: The calculation is mathematically exact, provided the input values are accurate and represent a valid arithmetic progression.

Q5: Can this be used for non-integer terms?
A: Yes, the formula works for both integer and non-integer values, including decimal numbers.