Enter the first term, position of the term, and the common difference into the calculator to determine the Nth term in a sequence.

Nth Term Test Formula

The following formula is used to calculate the Nth term in a sequence. 

Tn = a + (n - 1) * d

Variables:

  • Tn 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

To calculate the Nth term in a sequence, subtract 1 from the position of the term in the sequence, then multiply the result by the common difference between the terms. Add this result to the first term in the sequence.

What is a 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.

How to Calculate Nth Term Test?

The following steps outline how to calculate the Nth Term using the formula: Tn = a + (n – 1) * d.

  1. First, determine the value of the first term (a).
  2. Next, determine the position of the term in the sequence (n).
  3. Next, determine the common difference between the terms in the sequence (d).
  4. Use the formula Tn = a + (n – 1) * d to calculate the Nth term.
  5. After inserting the values of a, n, and d into the formula, calculate the result.

Example Problem:

Use the following variables as an example problem to test your knowledge.

First term (a) = 3

Position of the term (n) = 5

Common difference (d) = 2