13–20. Explicit formulas Write the first four terms of the sequence { aₙ }∞ₙ₌₁. 
aₙ = 1/10ⁿ

Verified step by step guidance

1. Identify the general term of the sequence given by the explicit formula \(a_n = \frac{1}{10^n}\), where \(n\) is the term number starting from 1.
2. To find the first term \(a_1\), substitute \(n=1\) into the formula: \(a_1 = \frac{1}{10^1}\).
3. To find the second term \(a_2\), substitute \(n=2\) into the formula: \(a_2 = \frac{1}{10^2}\).
4. To find the third term \(a_3\), substitute \(n=3\) into the formula: \(a_3 = \frac{1}{10^3}\).
5. To find the fourth term \(a_4\), substitute \(n=4\) into the formula: \(a_4 = \frac{1}{10^4}\).

Key Concepts

Sequences and Terms

A sequence is an ordered list of numbers defined by a specific rule. Each number in the sequence is called a term, denoted as aₙ, where n indicates the term's position. Understanding how to identify and write terms from a given formula is fundamental.

Explicit Formula for a Sequence

An explicit formula defines the nth term of a sequence directly in terms of n, allowing calculation of any term without knowing previous terms. For example, aₙ = 1/10ⁿ means each term is the reciprocal of 10 raised to the nth power.

Exponentiation and Powers of 10

Exponentiation involves raising a base number to a power, indicating repeated multiplication. Powers of 10 are especially important in sequences, as 10ⁿ means 10 multiplied by itself n times, affecting the size and pattern of the terms.