List the terms that complete a possible pattern in each of the following and state whether the pattern is arithmetic, geometric, or neither:
(a) 38, 33, 28, 23, 18, …
(b) 640, 320, 160, 80, …
(e) 1, ___, ___, ___ 25, 36, 49
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http://www.mathsisfun.com/numberpatterns.html
a)The pattern is continued by subtracting 5 each time.
b)The pattern is continued by dividing by 2 each time.
e)
1,4,9,16,25,36,49
In this series,all numbers are the squares of consecutive integers.
1^2=1
2^2=4
3^2=9
4^2=16
5^2=25
6^2=36
7^2=49
To determine the pattern in each sequence and find the missing terms, let's analyze each one individually:
(a) 38, 33, 28, 23, 18, ...
To find the missing terms and determine the pattern, we need to look for a consistent difference or ratio between consecutive terms.
The difference between each term in this sequence is -5 (subtracting 5 each time). Thus, the pattern is arithmetic with a common difference of -5.
Using the pattern, we can continue the sequence by subtracting 5 from the last given term of 18:
18 - 5 = 13
Therefore, the next terms could be 13, 8, 3, and so on.
(b) 640, 320, 160, 80, ...
Similarly, we need to find the difference or ratio between terms in this sequence.
The ratio between each term in this sequence is 1/2 (dividing by 2 each time). Thus, the pattern is geometric with a common ratio of 1/2.
Using the pattern, we can continue the sequence by multiplying the last given term of 80 by 1/2:
80 * (1/2) = 40
Therefore, the next terms could be 40, 20, 10, and so on.
(c) 1, ___, ___, ___ 25, 36, 49
To find the missing terms and determine the pattern, we need to look for a consistent difference or ratio between consecutive terms.
Observing the sequence, we can tell that the given terms are perfect squares. The pattern here is that the sequence begins with the square of 1 and increases by consecutive perfect squares.
Using this pattern, the missing terms can be filled as follows:
1^2 = 1
2^2 = 4
3^2 = 9
Therefore, the missing terms are 1, 4, 9.