Results:
Formulas used:
nth term: aₙ = a₁ + (n - 1)d
Sum: Sₙ = n(a₁ + aₙ) / 2
Welcome to our arithmetic sequence calculator! Whether you’re a student tackling homework or a professional dealing with data patterns, this tool will help you quickly solve arithmetic sequence problems. Let’s dive into how it works and why it’s so useful.
Formulas used:
nth term: aₙ = a₁ + (n - 1)d
Sum: Sₙ = n(a₁ + aₙ) / 2
An arithmetic sequence is a series of numbers where the difference between each consecutive term is constant. This constant difference is called the “common difference.” For example, in the sequence 2, 5, 8, 11, 14, the common difference is 3.
Our calculator will provide:
The formula for the nth term of an arithmetic sequence is:
aₙ = a₁ + (n - 1)d
Where:
To find the sum of the first n terms, we use:
Sₙ = n(a₁ + aₙ) / 2
Where:
Let’s work through an example:
Given: a₁ = 3, d = 2, n = 5
Find the 5th term: a₅ = 3 + (5 - 1)2 = 3 + 8 = 11
Calculate the sum of the first 5 terms: S₅ = 5(3 + 11) / 2 = 5(14) / 2 = 35
Our calculator would instantly provide these results for you!
Arithmetic sequences are not just classroom concepts; they have real-world applications:
A: Yes, if the first term is negative or if subtracting the common difference leads to negative values.
A: You can use our calculator to work backwards. Input the known term as a₁ and adjust n accordingly.
A: Subtract the earlier term from the later term and divide by the number of steps between them.
A: Absolutely! Arithmetic sequences can have fractional or decimal common differences.
A: Our calculator is designed to handle a large number of terms, but for extremely large sequences, consider breaking them into smaller parts for more manageable calculations.
Now that you understand how arithmetic sequences work and how our calculator can help, why not give it a try? Whether you’re checking homework, planning finances, or just exploring mathematical patterns, our arithmetic sequence calculator is here to make your calculations quick and easy.
Start using our calculator now and simplify your arithmetic sequence problems in seconds!
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