ARITHMETIC PROGRESSION
Arithmetic Sequences
An Arithmetic
Sequence is made by adding the same value each time.
Example:
1, 4, 7, 10, 13, 16, 19, 22, 25, ...
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This sequence has a difference of 3 between each number.
The pattern is continued by adding 3 to the last number each time, like this:
The pattern is continued by adding 3 to the last number each time, like this:
Example:
3, 8, 13, 18, 23, 28, 33, 38, ...
|
This sequence has a difference of 5 between each number.
The pattern is continued by adding 5 to the last number each time, like this:
The pattern is continued by adding 5 to the last number each time, like this:
The value added each time is called the "common
difference"
What is the common difference in this example?
19, 27, 35, 43, ...
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Answer: The common difference is 8
The common difference could also be negative:
Example:
25, 23, 21, 19, 17, 15, ...
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This common difference is −2
The pattern is continued by subtracting 2 each time, like this:
The pattern is continued by subtracting 2 each time, like this:
Special Sequences
1, 3, 6, 10, 15, 21, 28, 36, 45, ...
|
This Triangular
Number Sequence is generated from a pattern of dots which form a
triangle.
By adding another row of dots and counting all the dots we
can find the next number of the sequence:
Square Numbers
0, 1, 4, 9, 16, 25, 36, 49, 64, 81, ...
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They are the squares of whole
numbers:
0 (=0×0)
1 (=1×1)
4 (=2×2)
9 (=3×3)
16 (=4×4)
etc...
1 (=1×1)
4 (=2×2)
9 (=3×3)
16 (=4×4)
etc...
Cube Numbers
1, 8, 27, 64, 125, 216, 343, 512, 729, ...
|
They are the cubes of the
counting numbers (they start at 1):
1 (=1×1×1)
8 (=2×2×2)
27 (=3×3×3)
64 (=4×4×4)
etc...
8 (=2×2×2)
27 (=3×3×3)
64 (=4×4×4)
etc...
Fibonacci Numbers
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...
|
The Fibonacci
Sequence is found by adding the two numbers before it together.
The 2 is found by adding the two numbers before it (1+1)
The 21 is found by adding the two numbers before it (8+13)
The next number in the sequence above would be 55 (21+34)
Can you figure out the next few numbers?
QUESTION
Q.1
Q.2
Q.3
The 2 is found by adding the two numbers before it (1+1)
The 21 is found by adding the two numbers before it (8+13)
The next number in the sequence above would be 55 (21+34)
Can you figure out the next few numbers?
QUESTION
Q.1
What is the sum of the eleventh to twentieth terms (inclusive)of the arithmetic sequence
7, 12, 17, 22, ... ?
7, 12, 17, 22, ... ?
A
154
B
295
C
795
D
1,090
Q.2
What is the fiftieth term of the arithmetic sequence 3, 7, 11, 15, ... ?
A
53
B
151
C
199
D
203
Q.3
What is the thirty-second term of the arithmetic sequence -12, -7, -2, 3, ... ?
A
143
B
148
C
153
D
167
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