Understanding and Calculating the 15th Term of a Sequence: 3n4

Sequences are a fundamental concept in mathematics, often used in various fields such as computer science, physics, and finance. A sequence is an ordered list of numbers. Each number in a sequence can be represented by a formula, known as the nth term formula. In this article, we will explore a specific sequence where the nth term formula is given as 3n4. We will then focus on calculating the 15th term of this sequence.

What is a Sequence?

A sequence is a list of numbers arranged in a specific order. An element in a sequence is often denoted as an, where n represents the position of the element in the sequence. To fully understand a sequence, it is crucial to know its nth term formula, which describes how to calculate any term in the sequence based on its position.

Introduction to the Formula

The given nth term formula for our sequence is 3n4. This means that each term in the sequence is calculated by raising the position, n, to the fourth power and then multiplying by 3.

Understanding the 15th Term

Given the formula 3n4, we can calculate the value of the 15th term in the sequence by substituting n with 15. Let's break this down step-by-step:

Substitute n with 15 in the formula 3n4. Raise 15 to the fourth power: 154. Multiply the result by 3.

The calculations are as follows:

154 15 times; 15 times; 15 times; 15 50625 3 times; 50625 151875

Therefore, the 15th term of the sequence is 151875.

Additional Insights and Applications

Understanding the 15th term is just the beginning. Sequences with formulas such as 3n4 have unique properties and can be used to model and solve a variety of real-world problems.

Calculating the 15th Term: Manual Method

Let's walk through the manual calculation of the 15th term:

Identify the formula: nth term 3n4. Substitute n with 15: 3(154) Calculate 154: 15 times; 15 times; 15 times; 15 Multiply the result by 3: 3 times; 50625 151875

By following these steps, we can accurately calculate the 15th term.

Calculating the 15th Term: Using a Calculator

For a more straightforward approach, you can use a calculator or programming language to compute the 15th term:

n  15
result  3 * (n ** 4)
print(result)

This code will output the value 151875, the same as our manual calculation.

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Related Keywords

sequence calculation 15th term nth term formula

Understanding the formula for any sequence and calculating specific terms, such as the 15th term, is a fundamental skill in mathematics. By applying the nth term formula, you can uncover the hidden patterns and relationships in a sequence, making it easier to solve complex problems and analyze data.

If you found this article helpful, consider exploring more resources on sequences and formulas. Understanding mathematical concepts can greatly enhance your problem-solving skills and provide a deeper insight into the world around us.

Stay curious and continue to explore the fascinating world of mathematics!