Calculators for Sequences and Series

I greet you this day,
You may use these calculators to check your answers. You are encouraged to solve the questions on your own first, before checking your answers with the calculators.
These topics are covered in my Notes and Videos on Sequences.
I wrote the codes for these calculators using Javascript, a client-side scripting language. Please use the latest Internet browsers. The calculators should work.
The Wolfram Alpha widget (many thanks to the developers) are used for some calculators.
For some calculations, you may need to refresh your browser after each calculation.
Comments, ideas, areas of improvement, questions, and constructive criticisms are welcome. You may contact me.
If you do, please be positive.
If you are my student, please do not contact me here. Contact me via the school's system.
Thank you for visiting.

Please NOTE:
(1.) Only integers and decimals are allowed. Fractions and variables are not allowed for this calculator.
If your answer is a decimal, and you need to convert it to a fraction, then use the Decimal to Fraction link.
(2.) If you are not sure of what type of sequence OR if you would like to know the general term of a particular sequence, begin with the What type of Sequence? link.
Thank you for visiting.

Samuel Dominic Chukwuemeka
(SamDom For Peace)
B.Eng., A.A.T, M.Ed., M.S

Arithmetic Sequence

Given: first term, common difference, number of terms
To Find: other details
First term is

Common difference is

Number of terms is

Given: first term, last term, number of terms
To Find: other details
First term is

Last term is

Number of terms is

Given: first term, second term, last term
To Find: other details
First term is

Second term is

Last term is

Given: first term, common difference, sum of $n$ terms
To Find: other details
First term is

Common difference is

Sum of the first $n$ terms is

Given: first term, last term, sum of the first $n$ terms
To Find: other details
First term is

Last term is

Sum of the first $n$ terms is
Given: any two terms
To Find: the common difference, first term
The th term is

The th term is

Given: any two terms
To Find: any $nth$ term, sum of the first any $n$ terms
The th term is

The th term is

The th term is

The sum of the first terms is

Given: At least two terms of the Arithmetic Sequence
To Find: the general term of the sequence, list all the terms of the sequence up to a specific term, the sum of the first specific term of the sequence
List all the terms of the arithmetic sequence up to the th term

The general term of the arithmetic sequence is: + $(n - 1)$

Given: lower limit ($n = 1$) and upper limit (a positive integer only) of a summation (sigma notation), $nth$ term
To Find: other details
$\Sigma$ $n+$

Given: lower limit (a positive integer greater than $1$ only) and upper limit (a positive integer only) of a summation (sigma notation), $nth$ term
To Find: other details
$\Sigma$ $n+$

Geometric Sequence

Given: first term, second term, number of terms
To Find: other details
First term is

Second term is

Number of terms is

Given: first term, common ratio, number of terms
To Find: other details
First term is

Common Ratio is

Number of terms is

Given: At least two terms of the Geometric Sequence
To Find: the general term of the sequence, list all the terms of the sequence up to a specific term, the sum of the first specific term of the sequence, the sum to infinity of the sequence
List all the terms of the geometric sequence up to the th term

The general term of the geometric sequence is: * ^{$n - 1$}

Given: any two terms
To Find: the common ratio, first term
The th term is

The th term is

Given: any two terms
To Find: any $nth$ term, sum of the first any $n$ terms
The th term is

The th term is

The th term is

The sum of the first terms is

Given: first term, common ratio
To Find: the sum to infinity
First term is

Common Ratio is

Given: sum to infinity, common ratio
To Find: the first term
Sum to infinity is

Common Ratio is

Given: sum to infinity, first term
To Find: the common ratio
Sum to infinity is

First term is

Quadratic Sequence

Given: At least three terms of the Quadratic Sequence
To Find: the general term of the sequence, list all the terms of the sequence up to a specific term
List all the terms of the quadratic sequence up to the th term

The general term of the quadratic sequence is: $n^2 +$ $n +$

Given: At least three terms of the Quadratic Sequence
To Find: the general term of the sequence, the value of a specific term, the term which gives a specific value, the term that has the least value, the least value
The general term of the quadratic sequence is: $n^2 +$ $n +$

The th term is

The th term and the th term has a value of

The vertex is ,

The term that has the least value is

The least value is

Triangular Number Sequence

Given: the number of terms
To Find: The $nth$ term, Sum of the first $n$ terms
The term is

The sum of the first terms is

List: all terms of the sequence up to a specific term
List all the terms of the triangular sequence up to the th term

Given: the $nth$ term
To Find: other details
The $nth$ term is

The number of terms is

The sum of the first terms is

Given: the sum of the first $n$ term
To Find: other details
The sum of the first $n$ terms is

The number of terms is

The term is

Square Number Sequence

Given: the number of terms
To Find: The $nth$ term, Sum of the first $n$ terms
The term is

The sum of the first terms is

List: all terms of the sequence up to a specific term
List all the terms of the square sequence up to the th term

Given: the $nth$ term
To Find: other details
The $nth$ term is

The number of terms is

The sum of the first terms is

Given: the sum of the first $n$ term
To Find: other details
The sum of the first $n$ terms is

The number of terms is

The term is

Cube Number Sequence

Given: the number of terms
To Find: The $nth$ term, Sum of the first $n$ terms
The term is

The sum of the first terms is

List: all terms of the sequence up to a specific term
List all the terms of the cube sequence up to the th term

Given: the $nth$ term
To Find: other details
The $nth$ term is

The number of terms is

The sum of the first terms is

Given: the sum of the first $n$ term
To Find: other details
The sum of the first $n$ terms is

The number of terms is

The term is

Recursive Sequence

First-Order Linear Recursive Sequence

Given: the next term of a linear recursive sequence in the form:
$r * RS_n + a$, the initial term, and the number of terms
To Find: The $nth$ term
The next term of a linear recursive sequence is: * $RS_n +$

The initial term is

The term is

Given: the next term of a linear recursive sequence in the form:
$r * RS_n + a$ the initial term, and the number of terms
List: all terms of the sequence up to a specific term
The next term of a linear recursive sequence is: * $RS_n +$

The initial term is

List all the terms of the sequence up to the th term

Fibonacci Sequence

Given: the number of terms
To Find: the $nth$ term, sum of the first $n$ terms
The th term is

The sum of the first terms is

List: all terms of the sequence up to a specific term
List all the terms of the Fibonacci sequence up to the th term