 # Level 5-6 Algebra - nth Term

You'll have found by now that algebra forms a major part of KS3 Maths. In algebra letters are used in place of numbers. The letter n (usually in italics) is often used to indicate the position of a term in a sequence. We call this the 'nth' term.

Finding the rule for a number pattern is usually quite easy but can sometimes be a bit harder. One famous pattern is the Fibonacci sequence. This describes a spiral pattern and is very common in nature. The rule for the Fibonacci sequence is to add the previous two numbers to find the next. The nth term for this would be... advanced mathematics. Don't worry about that just yet!

Here's an easier example. If a sequence begins with 5 and goes up in twos thereafter, the nth term of that sequence would be 2n + 3 (2 x 1 + 3 = 5, 2 x 2 + 3 = 7, 2 x 3 + 3 = 9 etc.). This can be a little difficult to grasp but work through this quiz (and read the helpful comments!) and you will soon get the idea.

1.
The nth term of a sequence is given by 3n + 1. What is the numeric value of the 1st term?
3
4
6
9
In the 1st term the value of n will be 1 and therefore the answer can be found as follows: (3 x 1) + 1
2.
The nth term of a sequence is (2n)2 + 1. What is the the numeric value of the 3rd term?
33
35
37
39
(2 x 3)2 + 1
3.
The nth term of a sequence is given by 3n + 1. What is the numeric value of the 8th term?
12
13
25
50
We are told that we need the 8th term. We put an 8 where the n is and then work it out: (3 x 8) + 1
4.
What is the next number in this sequence: 1, 4, 9, 16?
18
20
22
25
These are known as square numbers. The 1st number in the sequence is 1 x 1; the 2nd number is 2 x 2; the 3rd number is 3 x 3 etc.
5.
The nth term of a sequence is given by 14n - 6. What is the numeric value of the 2nd term?
8
20
22
24
(14 x 2) - 6
6.
The nth term of a sequence is (n + 1)2. What is the the numeric value of the 4th term?
20
25
30
35
(4 + 1)2
7.
What is the next number in this sequence: 1, 1, 2, 3, 5, 8?
12
13
14
15
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)
8.
The nth term of a sequence is given by 3n + 1. What is the numeric value of the 3rd term?
4
6
8
10
The answer can be found as follows: (3 x 3) + 1
9.
What is the nth term of the sequence 6, 11, 16, 21?
5n
5n + 1
5n + 5
n + 5
(5 x n) + 1
10.
What is the next number in this sequence: 1, 8, 27?
35
36
54
64
These are known as cube numbers. The 1st number in the sequence is 1 x 1 x 1; the 2nd number is 2 x 2 x 2; the 3rd number is 3 x 3 x 3 and the 4th number will be 4 x 4 x 4
Author:  Frank Evans