If there is one prayer that you should pray/sing every day and every hour, it is the LORD's prayer (Our FATHER in Heaven prayer)
It is the most powerful prayer. A pure heart, a clean mind, and a clear conscience is necessary for it.
- Samuel Dominic Chukwuemeka

For in GOD we live, and move, and have our being. - Acts 17:28

The Joy of a Teacher is the Success of his Students. - Samuel Chukwuemeka

# Calculators for Sequences and Series I greet you this day,
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.

(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

## Decimal to Fraction

• Given: A decimal (positive decimals only)
To Convert: to a simplified fraction
• $=$

## What type of Sequence?

• Given: Only the first three or four terms of the Sequence (no less than three terms or no more than four terms)

Begin by typing only the first three terms.
If you type only three terms and the answer is undefined, then include the fourth term.

To Find: the type of sequence, the general term of the sequence

## Arithmetic Sequence

• Given: first term, common difference, number of terms
To Find: other details
• Given: first term, last term, number of terms
To Find: other details
• Given: first term, second term, last term
To Find: other details
• Given: first term, common difference, sum of $n$ terms
To Find: other details
• Given: first term, last term, sum of the first $n$ terms
To Find: other details
• 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 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 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) of a summation (sigma notation), $nth$ term
To Find: other details
•  $\Sigma$ $n+$

• Given: lower limit (a positive integer greater than $1$) and upper limit (a positive integer) 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
• Given: first term, common ratio, number of terms
To Find: other details
• 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 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 sum of the first terms is

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

• 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 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 and the th term has a value of

The vertex is ,

The term that has the least value is

The least value is

## Write the $nth$ term of "other" Sequences

This calculator will:
(1.) Write the explicit formula of some sequences.
The $nth$ or general term of the sequence is the Closed form: in the answer.
You may review the Continuation: to see more terms of the sequence.

If the sequence is long, you may type it in the big textbox, then copy and paste it in the textbox of the calculator.
Click the "Submit" button.

Sequence: