I need help with sequences
2,1,1/2,1/4,...
Is this arithmetic, geometric,neither, or both (geometric?)
7,9,11,13
arithmetic, geometric,neither, or both.
(arithmetic?)
1,2,4,8...
Whats the rule think the rule is: Start with one and multiply by two repeatedly
50,40,30,20
Rule Start with 50 and subtract ten repeatedly
Find the next three terms in the sequence
1,1,2,3,5,8..(11,14,17)
I put my answers, can someone please check them?
Thanks in advanced
The first 4 are all ok.
The last one is the Fibonacci Sequence, where each term is the sum of the two previous terms. It goes
1,1,2,3,5,8,13,21,34,55,...
Your constant d=3 is just based on the terms 5,8 but clearly does not hold for the earlier terms.
I'm confused :|
Let's go through each sequence and determine their types and rules.
1) 2, 1, 1/2, 1/4,...
To determine the type of this sequence, we can calculate the ratio between consecutive terms.
2/1 = 2
1/2 = 0.5
1/4 = 0.25
The ratio between consecutive terms is not constant. Instead, it is decreasing by a factor of 0.5 each time. Therefore, this sequence is a geometric sequence.
2) 7, 9, 11, 13
Similarly, we calculate the differences between consecutive terms.
9 - 7 = 2
11 - 9 = 2
13 - 11 = 2
The differences are constant, so this sequence is an arithmetic sequence.
3) 1, 2, 4, 8...
The terms in this sequence seem to be doubling each time. To confirm, we can calculate the ratios between consecutive terms.
2/1 = 2
4/2 = 2
8/4 = 2
The ratio is constant at 2, so this is a geometric sequence where each term is obtained by multiplying the previous term by 2.
4) 50, 40, 30, 20
The differences between consecutive terms are:
40 - 50 = -10
30 - 40 = -10
20 - 30 = -10
The differences are constant, but negative. This means that each term is obtained by subtracting 10 from the previous term. Thus, this sequence is an arithmetic sequence with a common difference of -10.
Now let's find the next three terms in the sequence 1, 1, 2, 3, 5, 8...
To determine the pattern of this sequence, we can see that each term is the sum of the previous two terms. This is known as the Fibonacci sequence. Therefore, the next three terms would be:
8 + 5 = 13
5 + 8 = 13
8 + 13 = 21
So, the next three terms in the sequence are 13, 13, 21.
Hope this clarifies things for you!