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Level 5-6 Algebra - nth Term

Explore number patterns and find their nth term. Learn how to predict future numbers in a sequence using clear algebraic rules in KS3 Maths.

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Fascinating Fact:

Triangular numbers count dots in a triangle. The sequence 1, 3, 6, 10 has nth term n(n + 1)÷2, so the 20th term equals 210.

In KS3 Maths, students learn how to use algebra to describe number patterns. The nth term formula helps you find any term in a sequence without listing them all.

Key Terms

Sequence: A list of numbers that follow a particular rule or pattern.
nth term: A formula that gives the value of any term in a sequence using its position number, n.
Arithmetic sequence: A sequence that increases or decreases by the same amount each time.

Frequently Asked Questions (Click to see answers)

How do I find the nth term of a sequence?

Find the common difference between terms, multiply it by n, and adjust by adding or subtracting to match the sequence’s starting number.

What does the nth term formula mean?

The nth term formula shows how each term changes with position. For example, if the formula is 3n + 1, you multiply the position by 3 and add 1.

What are triangular numbers in KS3 Maths?

Triangular numbers form a pattern of dots that make triangles. Their nth term is n(n + 1)÷2, giving 1, 3, 6, 10, 15, and so on.

Try These Related Quizzes

1 .

The nth term of a sequence is (n + 1)². What is the the numeric value of the 4^th term?

(4 + 1)²

2 .

What is the next number in this sequence: 1, 8, 27?

These are known as cube numbers. The 1^st number in the sequence is 1 x 1 x 1; the 2^nd number is 2 x 2 x 2; the 3^rd number is 3 x 3 x 3 and the 4^th number will be 4 x 4 x 4

3 .

The nth term of a sequence is (2n)² + 1. What is the the numeric value of the 3^rd term?

(2 x 3)² + 1

4 .

The nth term of a sequence is given by 3n + 1. What is the numeric value of the 3^rd term?

The answer can be found as follows: (3 x 3) + 1

5 .

What is the next number in this sequence: 1, 1, 2, 3, 5, 8?

This is known as the Fibonacci sequence. To find each number you add together the two previous numbers. After 13 comes 21 (8 + 13) and then comes 34 (21 + 13)

6 .

The nth term of a sequence is given by 3n + 1. What is the numeric value of the 8^th term?

We are told that we need the 8^th term. We put an 8 where the n is and then work it out: (3 x 8) + 1

7 .

What is the nth term of the sequence 6, 11, 16, 21?

5n + 1

5n + 5

n + 5

(5 x n) + 1

8 .

What is the next number in this sequence: 1, 4, 9, 16?

These are known as square numbers. The 1^st number in the sequence is 1 x 1; the 2^nd number is 2 x 2; the 3^rd number is 3 x 3 etc.

9 .

The nth term of a sequence is given by 3n + 1. What is the numeric value of the 1^st term?

In the 1^st term the value of n will be 1 and therefore the answer can be found as follows: (3 x 1) + 1

10 .

The nth term of a sequence is given by 14n - 6. What is the numeric value of the 2^nd term?

(14 x 2) - 6

You can find more about this topic by visiting BBC Bitesize - Algebraic terms and expressions

Author: Frank Evans (Specialist 11 Plus Teacher and Tutor)

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