Answers:
<h2>C & D</h2>
Step-by-step explanation:
There are two general types of sequences that follow a pattern, geometric and arithmetic. Let's see the difference between the two:
An arithmetic sequence is produced by adding the same number to all the terms in the sequence.
EXAMPLE:
5, 7, 9, 11, 13, 15, 17 (The number 2 is added to all terms)
To figure out if a sequence is arithmetic, subtract the first term from the second, then the second from the third and so on until you have checked all the terms.
7 - 5 = 2
9 - 7 = 2
11 - 9 = 2
13 - 11 = 2
15 - 13 = 2
17 - 15 = 2
All results equal 2, so the sequence is arithmetic
From your list: The following sequences are arithmetic
A. 5, 10, 15, 20, 25 (common difference of 5)
The next type of sequence is the geometric sequence.
A geometric sequence is produced when the all the terms in the sequence are multiplied or divided by the same number.
EXAMPLE:
100, 50, 25 (Each term is divided by 2)
To figure this out, we divide each term in the sequence by the next term.
100 / 50 = 2
50 / 25 = 2
All results are two, so this sequence can be confirmed to be geometric
From your list: The following sequences are geometric
C. 10, 5, 2.5, 1.25, 0.625, 0.3125 (common quotient of 2)
D. -9, -3, -1, -1/3, -1/9, -1/27 (common quotient of -3)
There is one final type of sequence, which has no common difference, sum, quotient, or product.
EXAMPLE:
5, 6, 8, 9, 11, 12, 14, 15
This sequence has a pattern, the differences between the numbers are not common.
6 - 5 = 1
8 - 6 = 2
9 - 8 = 1
11 - 9 = 2
12 - 11 = 1
14 - 12 = 2
15 - 14 = 1
From your list: The following sequences are neither geometric nor arithmetic
B. 1, 1, 2, 3, 5, 8, 13 (No pattern)
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