MATH CALCULATOR
Arithmetic Sequence Calculator
Calculate the nth term and sum of an arithmetic sequence with our online tool.
What is the Arithmetic Sequence Calculator & How does it work?
An arithmetic sequence is a sequence of numbers in which each term after the first is obtained by adding a constant, called the common difference, to the previous term. For example, in the sequence 2, 5, 8, 11, …, the common difference is 3.
The nth term of an arithmetic sequence can be calculated using the formula:
The sum of the first n terms of an arithmetic sequence can be calculated using the formula:
The nth term of an arithmetic sequence can be calculated using the formula:
a_n = a_1 + (n – 1) cdot d
a_n = nth term, a_1 = first term, n = term number, d = common difference
The sum of the first n terms of an arithmetic sequence can be calculated using the formula:
S_n = frac{n}{2} cdot (a_1 + a_n)
S_n = sum of first n terms, a_1 = first term, n = number of terms, a_n = nth term
Parameters
Result—
Frequently Asked Questions
How do I find the nth term of an arithmetic sequence?
Use the formula a_n = a_1 + (n - 1) * d, where a_n is the nth term, a_1 is the first term, n is the term number, and d is the common difference.
What is the sum of the first n terms in an arithmetic sequence?
The sum can be calculated using the formula S_n = n/2 * (a_1 + a_n), where S_n is the sum, n is the number of terms, a_1 is the first term, and a_n is the nth term.
Can you explain what an arithmetic sequence is?
An arithmetic sequence is a series of numbers where each term after the first is found by adding a constant, called the common difference, to the previous term.
How do I find the common difference in an arithmetic sequence?
Subtract any term from the term that follows it. For example, if your sequence is 2, 5, 8, 11, ..., the common difference d is 5 - 2 = 3.
What is an example of an arithmetic sequence?
An example of an arithmetic sequence is 2, 5, 8, 11, ..., where each term increases by a common difference of 3.
How can I use this calculator to find the sum of the first 10 terms if my sequence starts at 3 and has a common difference of 4?
Input the first term (3), the common difference (4), and the number of terms (10) into the calculator. It will then compute the sum for you.
Is there a formula to find the nth term if I know the sum of the first n terms?
Yes, but it involves solving a quadratic equation derived from the sum formula S_n = n/2 * (2a_1 + (n - 1)d).
Results are for informational purposes only and do not constitute professional advice.