Nth term of the sequence

Definition

The nth term of a sequence is a formula that describes the value of the term at position n. It allows you to find any term in the sequence without listing all the preceding terms.

5 Must Know Facts For Your Next Test

1. The nth term formula can be arithmetic, geometric, or follow another pattern depending on the type of sequence.
2. For an arithmetic sequence, the nth term is often given by $a_n = a_1 + (n-1)d$ where $a_1$ is the first term and $d$ is the common difference.
3. For a geometric sequence, the nth term is commonly expressed as $a_n = a_1 \cdot r^{(n-1)}$ where $a_1$ is the first term and $r$ is the common ratio.
4. Finding the nth term can help in summing sequences using formulas like those for arithmetic and geometric series.
5. Understanding how to derive and use the nth term formula is essential for solving problems involving sequences and series.

Review Questions

• What is the formula for finding the nth term in an arithmetic sequence?
• How do you find the nth term of a geometric sequence?
• Why is knowing the nth term useful when dealing with sequences?

Related terms

Arithmetic Sequence: A sequence in which each term after the first is obtained by adding a constant difference to its predecessor.

Geometric Sequence: A sequence where each term after the first is found by multiplying its predecessor by a fixed, non-zero number called the common ratio.

Series: $\text{The sum of terms in a sequence.}$