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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 .
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.
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 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.
4 .
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.
5 .
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.
6 .
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.
7 .
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.
8 .
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.
9 .
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.
10 .
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.
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