Here is a sequence of numbers.
7, 5, 3, 1, – 1, …
Find the next term in this sequence.
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Sequences
Here is a sequence of numbers.
7, 5, 3, 1, – 1, …
Find the next term in this sequence.
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Write the next term in each of these sequences.
[1]
[1]
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This expression can be used to generate a sequence of numbers.
[2]
[2]
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Find the th term of the sequence below.
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The th term of a sequence is
i)
Find the 2nd term.
[1]
ii)
Find the value of when the th term is 498.
.................................................. [3]
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Here is a sequence.
Find the value of and the value of .
...........................................
...........................................
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Find the th term of each sequence.
4 2 0 -2 -4 ...
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1 7 17 31 49 ...
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Complete the table for the 5th term and the nth term of each sequence.
1st term | 2nd term | 3rd term | 4th term | 5th term | th term | |
9 | 5 | 1 | -3 | |||
4 | 9 | 16 | 25 | |||
1 | 8 | 27 | 64 | |||
8 | 16 | 32 | 64 |
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0, 1, 1, 2, 3, 5, 8, 13, 21 , ...
This sequence is a Fibonacci sequence.
After the first two terms, the rule to find the next term is “add the two previous terms”.
For example, 5 + 8 = 13.
Use this rule to complete each of the following Fibonacci sequences.
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Find the th term of the sequence below.
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Find the th term of each sequence.
[2]
[2]
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Find the th term of the sequence below.
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These are the first four diagrams of a sequence.
The diagrams are made from white dots and black dots.
Complete the table for Diagram 5 and Diagram 6.
Diagram | 1 | 2 | 3 | 4 | 5 | 6 |
Number of white dots | 1 | 4 | 9 | 16 | ||
Number of black dots | 0 | 1 | 3 | 6 | ||
Total number of dots | 1 | 5 | 12 | 22 |
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Write an expression, in terms of , for the number of white dots in Diagram
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The expression for the total number of dots in Diagram is .
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is the total number of dots used to make all of the first diagrams.
Find the value of and the value of .
You must show all your working.
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................................................
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The table shows the first four terms in sequences A, B, and C.
Sequence | 1st term | 2nd term | 3rd term | 4th term | 5th term | th term | |
A | 4 | 9 | 14 | 19 | |||
B | 3 | 10 | 29 | 66 | |||
C | 1 | 4 | 16 | 64 |
Complete the table.
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The table shows the first five terms of sequences A, B and C.
Sequence | 1st term | 2nd term | 3rd term | 4th term | 5th term | 6th term |
A | 0 | 1 | 4 | 9 | 16 | |
B | 4 | 5 | 6 | 7 | 8 | |
C | -4 | -4 | -2 | 2 | 8 |
Complete the table.
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Find an expression for the th term of
i)
sequence A,
[2]
ii)
sequence B.
[1]
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Find the value of when the th term of sequence A is 576.
...............................................
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i)
Find an expression for the th term of sequence C.
Give your answer in its simplest form.
[3]
ii)
Find the value of the 30th term of sequence C.
[2]
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