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How to Find the Nth Term: Quadratic and Other Sequences Explained for Kids

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Poppy

6/25/2022

Maths

Nth term

How to Find the Nth Term: Quadratic and Other Sequences Explained for Kids

The document provides an overview of different types of sequences, focusing on quadratic sequences and their nth term formulas. It covers arithmetic, geometric, Fibonacci, square, and triangular numbers, explaining their characteristics and providing examples. The text also details methods for finding the nth term of linear and quadratic sequences, including step-by-step explanations and examples.

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6/25/2022

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Maths

779

Jun 25, 2022

1 page

How to Find the Nth Term: Quadratic and Other Sequences Explained for Kids

The document provides an overview of different types of sequences, focusing on quadratic sequences and their nth term formulas. It covers arithmetic, geometric, Fibonacci, square, and triangular numbers, explaining their characteristics and providing examples. The text also details methods for... Show more

Quadratic Sequences
Arithmetic/Line
difference between consecutive numbers
18
Quadratic-2nd difference between consecutive numbers is
4, 25

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Quadratic Sequences and Other Sequence Types

This page provides a comprehensive overview of various sequence types, with a focus on quadratic sequences and methods for finding their nth terms. It covers essential concepts in sequence analysis, making it valuable for students studying mathematics.

The document begins by introducing different types of sequences:

  1. Arithmetic LinearLinear Sequences: These have a constant difference between consecutive terms.
  2. Quadratic Sequences: The second difference between consecutive terms is constant.
  3. Geometric Sequences: Each term after the first is found by multiplying the previous one by a fixed, non-zero number called a common ratio.
  4. Fibonacci Sequence: Each number is the sum of the two preceding ones.
  5. Square Numbers: The product of an integer with itself.
  6. Triangular Numbers: A series obtained by continued summation of natural numbers.

Definition: A quadratic sequence is a sequence where the second difference between consecutive terms is constant.

The page then delves into the methods for finding the nth term of sequences:

For linear sequences:

  • The document provides an example of finding the nth term, explaining how to use the common difference to formulate the expression.

Example: For the sequence 6, 12, 18, 24, the nth term is 6n.

For quadratic sequences:

  • The general rule for the nth term of a quadratic sequence is presented as an² + bn + c.
  • A step-by-step method for finding the values of a, b, and c is demonstrated.

Highlight: The second difference in a quadratic sequence is always twice the 'a' value in the nth term formula.

The document concludes with an alternative method for finding the nth term of quadratic sequences by comparison, using square numbers as an example.

Example: For the sequence 9, 16, 25..., the nth term is Tnn = n².

This comprehensive guide serves as an excellent resource for students learning about finding the nth term of a quadratic sequence and other sequence types, providing clear explanations and practical examples.

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The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.

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This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.

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Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.

Anna

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I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️

Thomas R

iOS user

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Brad T

Android user

Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍

David K

iOS user

The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!

Sudenaz Ocak

Android user

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Greenlight Bonnie

Android user

I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend

Aubrey

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Marco B

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Elisha

iOS user

This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!

Paul T

iOS user