Nth Term Formula

Definition

The nth term formula, also known as the general term formula, is a mathematical expression that allows you to determine the value of any term in an arithmetic sequence. It provides a concise way to represent the pattern of the sequence and calculate the value of any specific term without having to list out the entire sequence.

5 Must Know Facts For Your Next Test

1. The nth term formula for an arithmetic sequence is $a_n = a_1 + (n-1)d$, where $a_n$ is the nth term, $a_1$ is the first term, and $d$ is the common difference.
2. The nth term formula allows you to calculate the value of any term in the sequence without having to list out all the previous terms.
3. The common difference, $d$, represents the constant change between consecutive terms in the arithmetic sequence.
4. The position of the term within the sequence, $n$, is used in the formula to determine the value of the nth term.
5. The nth term formula is a powerful tool for analyzing and working with arithmetic sequences, as it provides a concise and efficient way to generate any term in the sequence.

Review Questions

• Explain how the nth term formula is used to determine the value of a specific term in an arithmetic sequence.
  • The nth term formula, $a_n = a_1 + (n-1)d$, allows you to calculate the value of any term in an arithmetic sequence by using the position of the term within the sequence (n), the first term (a_1), and the common difference (d). To find the value of the nth term, you simply plug these values into the formula and solve for a_n. This formula is particularly useful when you need to find the value of a term that is not the first or second term in the sequence, as it eliminates the need to list out all the previous terms.
• Describe the relationship between the common difference and the nth term formula in an arithmetic sequence.
  • The common difference, $d$, is a crucial component of the nth term formula, $a_n = a_1 + (n-1)d$, for an arithmetic sequence. The common difference represents the constant change between any two consecutive terms in the sequence. This value is used in the formula to determine how the terms increase or decrease as you move from one term to the next. The common difference allows the formula to accurately calculate the value of the nth term based on its position in the sequence and the pattern established by the first term and the common difference.
• Analyze how the nth term formula can be used to identify the pattern of an arithmetic sequence and make predictions about future terms.
  • The nth term formula, $a_n = a_1 + (n-1)d$, provides a concise way to represent the pattern of an arithmetic sequence. By examining the formula, you can identify the first term ($a_1$) and the common difference ($d$), which together define the pattern of the sequence. With this information, you can use the formula to predict the value of any future term in the sequence, simply by substituting the appropriate value of $n$. This allows you to anticipate the behavior of the sequence and make informed decisions or calculations based on the pattern established by the nth term formula.

Related terms

Arithmetic Sequence:

An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant.

Common Difference:

The common difference in an arithmetic sequence is the constant difference between any two consecutive terms.

Explicit Formula:

The explicit formula, or the nth term formula, is a formula that allows you to find the value of any term in an arithmetic sequence using the position of the term within the sequence.