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Level 5-6 Algebra - nth Term
Discovering algebra is a big part of KS3 Maths. In algebra, we use letters instead of numbers. For example, the letter 'n' (often in italics) shows where a term is in a sequence, and we call it the 'nth' term.
Figuring out the rule for a number pattern can be easy or a bit tricky. Have you heard of the Fibonacci sequence? It creates a cool spiral pattern seen in nature. The rule: add the previous two numbers to find the next one. The nth term? Well, that's for advanced maths - no need to worry about that just yet!
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1 .
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.
2 .
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
3 .
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
4 .
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)
5 .
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
6 .
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
7 .
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
8 .
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
9 .
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
10 .
What is the nth term of the sequence 6, 11, 16, 21?
5n
5n + 1
5n + 5
n + 5
(5 x n) + 1
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