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# Number Sequences (Medium)

A number sequence involves following a pattern. Spotting the pattern is the key! For example, in the sequence 8, 16, 32, 64, ... each number in the sequence can be got from the previous term by multiplying by 2. In this case, the rule is: multiply by 2. The numbers in a sequence are called 'terms': in 5, 10, 15, 20, ... '5' is the first term and '15' is the third term.

If you want to talk about a term without naming it, you call it the nth term. For example, if n = 3, this is the 3rd term. In this quiz you will get some practice in using the rules for sequences.

TIP: To form a sequence from a given rule for the nth term, put n = 1 first, then n = 2, then n = 3 and so on - depending on how many terms you are asked to find. If you are asked to find 5 terms, then you will go as far as n = 5.

1.
Which sequence can be formed from the given rule for the nth term?
nth term = 4n + 7
11, 15, 18, 23, ...
11, 13, 15, 19, ...
11, 15, 19, 23, ...
11, 12, 15, 19, ...
The terms of the sequence are found by first putting n = 1, then n = 2, then n = 3 and finally n = 4 in the rule for the nth term = 4n + 7. As follows (do the multiplication first THEN the addition):
n = 1 gives 4 × 1 + 7 = 11
n = 2 gives 4 × 2 + 7 = 15
n = 3 gives 4 × 3 + 7 = 19
n = 4 gives 4 × 4 + 7 = 23
2.
Which sequence can be formed from the given rule for the nth term?
nth term = n2 - n
0, 3, 8, 15, ...
0, 2, 6, 12, ...
0, 2, 4, 6, 8, ...
1, 3, 5, 7, ...
The terms of the sequence are found by first putting n = 1, then n = 2, then n = 3 and finally n = 4 in the rule for the nth term = n2 - n. As follows (do the multiplication first THEN the addition):
n = 1 gives 12 - 1 = 0
n = 2 gives 22 - 2 = 2
n = 3 gives 32 - 3 = 6
n = 4 gives 42 - 4 = 12
3.
Which sequence can be formed from the given rule for the nth term?
nth term = -5n
-5, -10, -15, -20, ...
5, 10, 15, 20, ...
0, -5, -10, -15, ...
-5, -25, -125, -625, ...
The terms of the sequence are found by first putting n = 1, then n = 2, then n = 3 and finally n = 4 in the rule for the nth term = -5n. As follows:
n = 1 gives -5 × 1 = -5
n = 2 gives -5 × 2 = -10
n = 3 gives -5 × 3 = -15
n = 4 gives -5 × 4 = -20
4.
Which sequence can be formed from the given rule for the nth term?
nth term = -n + 1
0, 1, 2, 3, ...
0, -1, -2, -3, ...
1, 2, 3, 4, ...
1, 3, 5, 7, ...
The terms of the sequence are found by first putting n = 1, then n = 2, then n = 3 and finally n = 4 in the rule for the nth term = -n + 1. As follows:
n = 1 gives -1 + 1 = 0
n = 2 gives -2 + 1 = -1
n = 3 gives -3 + 1 = -2
n = 4 gives -4 + 1 = -3
5.
Which sequence can be formed from the given rule for the nth term?
nth term = 2n + 3
1, 7, 9, 13, ...
1, 5, 7, 9, ...
2, 5, 7, 9, ...
5, 7, 9, 11, ...
The terms of the sequence are found by first putting n = 1, then n = 2, then n = 3 and finally n = 4 in the rule for the nth term = 2n + 3. As follows (do the multiplication first THEN the addition):
n = 1 gives 2 × 1 + 3 = 5
n = 2 gives 2 × 2 + 3 = 7
n = 3 gives 2 × 3 + 3 = 9
n = 4 gives 2 × 4 + 3 = 11
6.
Which sequence can be formed from the given rule for the nth term?
nth term = 2n - 1
1, 3, 5, 9, ...
1, 3, 5, 7, ...
0, 1, 3, 5, ...
1, 5, 15, 45, ...
The terms of the sequence are found by first putting n = 1, then n = 2, then n = 3 and finally n = 4 in the rule for the nth term = 2n -1. As follows (do the multiplication first THEN the subtraction):
n = 1 gives 2 × 1 - 1 = 1
n = 2 gives 2 × 2 - 1 = 3
n = 3 gives 2 × 3 - 1 = 5
n = 4 gives 2 × 4 - 1 = 7
7.
Which sequence can be formed from the given rule for the nth term?
nth term = 4n - 1
5, 7, 11, 15, ...
3, 7, 12, 15, ...
3, 8, 11, 15, ...
3, 7, 11, 15, ...
The terms of the sequence are found by first putting n = 1, then n = 2, then n = 3 and finally n = 4 in the rule for the nth term = 4n - 1. As follows (do the multiplication first THEN the subtraction):
n = 1 gives 4 × 1 - 1 = 3
n = 2 gives 4 × 2 - 1 = 7
n = 3 gives 4 × 3 - 1 = 11
n = 4 gives 4 × 4 - 1 = 15
8.
Which sequence can be formed from the given rule for the nth term?
nth term = n2
1, 4, 9, 16, ...
2, 4, 6, 8, ...
1, 2, 3, 4, ...
1, 8, 27, 64, ...
The terms of the sequence are found by first putting n = 1, then n = 2, then n = 3 and finally n = 4 in the rule for the nth term = n2. As follows:
n = 1 gives 12 = 1
n = 2 gives 22 = 4
n = 3 gives 32 = 9
n = 4 gives 42 = 16
9.
Which sequence can be formed from the given rule for the nth term?
nth term = 2n
2, 4, 8, 16, ...
3, 6, 9, 12, ...
1, 2, 4, 6, ...
2, 4, 6, 8, ...
The terms of the sequence are found by first putting n = 1, then n = 2, then n = 3 and finally n = 4 in the rule for the nth term = 2n. As follows:
n = 1 gives 2 × 1 = 2
n = 2 gives 2 × 2 = 4
n = 3 gives 2 × 3 = 6
n = 4 gives 2 × 4 = 8
10.
Which sequence can be formed from the given rule for the nth term?
nth term = 6n
6, 12, 18, 24, ...
0, 6, 12, 18, ...
2, 4, 6, 8, ...
1, 6, 12, 18, ...
The terms of the sequence are found by first putting n = 1, then n = 2, then n = 3 and finally n = 4 in the rule for the nth term = 6n. As follows (do the multiplication first THEN the addition):
n = 1 gives 6 × 1 = 6
n = 2 gives 6 × 2 = 12
n = 3 gives 6 × 3 = 18
n = 4 gives 6 × 4 = 24
Author:  Frank Evans