Nth Term Calculator

Formula

To calculate the Nth term (\(T_n\)):

\[ T_n = a + (n - 1) \times d \]

Where:

\(T_n\) is the Nth term in the sequence
\(a\) is the first term in the sequence
\(n\) is the position of the term in the sequence
\(d\) is the common difference between the terms in the sequence

What is the Nth Term Test?

The Nth Term Test, also known as the Test for Divergence, is a mathematical test used to determine whether an infinite series converges or diverges. It states that if the limit of the sequence of terms in an infinite series does not approach zero as \(n\) (the term number) approaches infinity, then the series must diverge. If the limit is zero, the test is inconclusive and the series may either converge or diverge.

Example Calculation 1

Let's assume the following values:

First Term (\(a\)) = 2
Position of Term (\(n\)) = 5
Common Difference (\(d\)) = 3

Using the formula:

\[ T_n = 2 + (5 - 1) \times 3 = 2 + 4 \times 3 = 2 + 12 = 14 \]

The Nth term is 14.

Example Calculation 2

Let's assume the following values:

First Term (\(a\)) = 1
Position of Term (\(n\)) = 10
Common Difference (\(d\)) = 2

Using the formula:

\[ T_n = 1 + (10 - 1) \times 2 = 1 + 9 \times 2 = 1 + 18 = 19 \]

The Nth term is 19.