Suppose the sequence { aₙ} is defined by the explicit formula aₙ = 1/n, for n=1, 2, 3, .....Write out the first five terms of the sequence.

Verified step by step guidance

1. Identify the given explicit formula for the sequence: \(a_n = \frac{1}{n}\), where \(n = 1, 2, 3, \ldots\).
2. Understand that to find the first five terms, you substitute \(n = 1, 2, 3, 4, 5\) into the formula.
3. Calculate the first term by substituting \(n=1\): \(a_1 = \frac{1}{1}\).
4. Calculate the second term by substituting \(n=2\): \(a_2 = \frac{1}{2}\).
5. Continue this process for \(n=3, 4, 5\) to find \(a_3 = \frac{1}{3}\), \(a_4 = \frac{1}{4}\), and \(a_5 = \frac{1}{5}\).

Key Concepts

Sequence Definition

A sequence is an ordered list of numbers defined by a specific rule or formula. Each term in the sequence is identified by its position, usually denoted by n. Understanding how to interpret the formula for aₙ allows you to find any term in the sequence.

Explicit Formula for Sequences

An explicit formula directly expresses the nth term of a sequence as a function of n. For example, aₙ = 1/n means the term at position n is the reciprocal of n. This formula helps compute terms without needing previous terms.

Evaluating Terms of a Sequence

To find specific terms, substitute the term number n into the explicit formula. For aₙ = 1/n, the first five terms are found by plugging in n = 1, 2, 3, 4, and 5, resulting in 1, 1/2, 1/3, 1/4, and 1/5 respectively.