Question

Use your own words to describe the range of a sequence.

Short answer

The range of the sequence is 7.

Step-by-step solution

Understanding the Sequence

The first step in finding the range of a sequence is to identify the sequence itself. A sequence is a list of numbers arranged in a specific order. For example, consider the sequence: 3, 7, 2, 9, 5.

Identifying Extremes

The range of a sequence is determined by the difference between its highest and lowest values. In our example sequence (3, 7, 2, 9, 5), identify the smallest number (which is 2) and the largest number (which is 9).

Calculating the Range

Subtract the smallest value from the largest value to find the range. This means we calculate 9 - 2.

Conclusion

The range is the result of the subtraction. In the example, 9 - 2 equals 7, so the range of the sequence is 7.

Key concepts

sequence in mathematics

In mathematics, a sequence is more than just a mere list of numbers. It is a carefully ordered set of numbers, much like beads on a string, where each number holds a specific place in the line-up. Sequences can be finite or infinite. Finite sequences have a set number of terms, like \(a_1, a_2, ..., a_n\). Infinite sequences go on forever. Examples include the sequence \(3, 7, 2, 9, 5\), which is finite with 5 terms, and the sequence of natural numbers \(1, 2, 3, \dots\) which is infinite.

Sequences often follow a specific rule or pattern. Understanding this pattern can be crucial when making predictions or calculations. For instance, arithmetic sequences have a constant difference between consecutive terms, like \(2, 4, 6, 8, \dots\), while geometric sequences have a constant ratio, like \(3, 9, 27, \dots\). Recognizing these patterns can simplify the task of determining various properties, such as the range of a sequence.

finding extremes in a sequence

Finding the extremes in a sequence involves pinpointing the highest and lowest values from the list of numbers. These extremes are crucial in many mathematical applications, as they reveal the span of the numbers' distribution within the sequence.

• The smallest value in a sequence is called the minimum.
• The largest value is known as the maximum.

In our example \(3, 7, 2, 9, 5\), the minimum is 2, and the maximum is 9. With these extremes identified, you now have the key components needed to calculate the range. By understanding how to spot these extremes, one can easily transform a complex list of numbers into manageable components for further calculations.

This skill is not only useful in school exercises but also in data analysis and real-world problem-solving, where understanding the full scope of your data set can provide essential insights.

calculating range

The range of a sequence is a simple yet powerful measure of how spread out the numbers are. Calculating the range involves subtracting the smallest number in the sequence from the largest one. This tells us how wide the sequence stretches from one end to the other.

Let's use the example \(3, 7, 2, 9, 5\) to see how it works:

• First, identify the maximum value, which is 9.
• Next, identify the minimum value, which is 2.
• Subtract the minimum from the maximum to find the range: \(9 - 2 = 7\).

The range here is 7, indicating the spread of our sequence from bottom to top.

Calculating the range helps in understanding the variability of data. It's particularly useful when assessing variability in data sets, like test scores or temperatures, helping to visualize the extent of fluctuations within the data. Through this straightforward subtraction, we derive important information at a glance.