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# Practice - Sequences - 05

Welcome young mathematicians, to another exciting maths challenge. This time we'll be diving into the wonderful world of sequences. Will they always compute? Will a pattern emerge victorious? Can you find the hidden nth term? Only a true maths wizard will rise to the occasion. So, gear up for some mathematical fun! Let's see if you can crack these 10 questions.
1.
What is the nth term of the sequence: 7, 12, 17, ?
n + 5
5n - 3
5n + 2
n - 2
You add 5 to each term for next value, to have this in nth term form is 5n + 2.
2.
If the nth term of a sequence is n2 + n + 1, what is the 6th term in the sequence?
41
42
43
44
Substitute n = 6 into the nth term: 62 + 6 + 1 = 43.
3.
What is the nth term of the sequence: 5, 10, 20, 40, 80?
2n + 3
5 x 2n-1
4n
3n + 2
A term in the sequence is calculated by multiplying 5 by 2 raised to power 'n-1'. So, the nth term is 5 x 2n-1.
4.
What is the 20th term in the sequence 6, 12, 24, 48?
3 x 220
220 + 3
23 x 20
320 x 2
Becase each term is double the previous term, each term is calculated by multiplying 3 by a power of 2. The first number is 3 x 21 = 6, so the 20th term is, therefore, 3 x 220.
5.
What is the 10th term in the sequence that starts 1, 6, 11, 16, ?
46
50
51
56
You add 5 for each next term. The nth term for this sequence is -4 + 5n. Thus 10th term is 46.
6.
What is the nth term of the sequence: 10, 7, 4, 1, -2, ?
3n + 7
7 - 3n
-3n + 13
n - 9
You subtract 3 from each term, to translate this into nth term form -3n + 13, so the first number is -3 + 13.
7.
If the nth term of a sequence is 4n + 1, what is the 5th term in the sequence?
20
21
22
23
Substitute n = 5 into the nth term: 4(5) + 1 = 21.
8.
What is the next number in the sequence: 3, 9, 18, 30, ?
45
42
44
46
It’s an arithmetic sequence 3 + 6 = 9, 9 + 9 = 18, 18 + 12 = 30. The difference is increasing by 3 every term. Thus, the next term is 30 + 15 = 45.
9.
What is the next number in the sequence: 2, 6, 18, 54, ?
160
162
158
168
In this sequence, each term is multiplied by 3 to find the next term, so the next term is 54 x 3 = 162.
10.
What is the next number in the sequence: 3, 8, 15, 24, ?
33
35
36
34
The nth term of this sequence is (n + 1)2 - 1. The next term would be 62 = 36 - 1 = 35.
Author:  Graeme Haw