a sequence begins -4,1,6,11
find the rule that generates the sequence. Then give the 5oth term is the sequence. What type of reasoning inductive or deductive, do you use when solving this problem?
Well, I must say, trying to find a pattern in a sequence can be a bit like searching for your missing sock in the dryer - a puzzling quest indeed! But fear not, for Clown Bot is here to bring some humor to the task.
Now, let's see if we can sniff out the rule of this sequence. If we take a closer look at the numbers, we can observe that each term is 5 more than the previous term. So, it seems that the rule here is to add 5 to each preceding term to get the next term.
To find the 50th term in this sequence, let's do some mathemagical calculations. The first term is -4, and for each subsequent term, we're adding 5. So, by following this pattern, we have:
-4 + (50 - 1) * 5 = -4 + 49 * 5 = -4 + 245 = 241
The 50th term in this sequence should be 241.
As for the type of reasoning used, when we deduced that the rule was to add 5 to each preceding term, we employed deductive reasoning. However, when determining the 50th term using that rule, we employed inductive reasoning by applying patterns observed in previous terms to predict upcoming ones. So, we can say that both types of reasoning were involved in solving this problem.
Hope my clownish explanation didn't get your head in a spin! Keep those chuckles coming!
To find the rule that generates the given sequence, we can observe the pattern between the terms. Here, we can see that each term increases by 5. So, the rule that generates the sequence is "add 5 to the previous term."
Using this rule, we can find the 50th term in the sequence by applying the rule multiple times. Let's do the calculation step by step:
- The first term is -4.
- To find the second term, we add 5 to the previous term: -4 + 5 = 1.
- To find the third term, we add 5 to the previous term: 1 + 5 = 6.
- To find the fourth term, we add 5 to the previous term: 6 + 5 = 11.
We can continue this pattern to find the 50th term in a similar manner:
- To find the 50th term, we add 5 to the previous term 49 times: 11 + (5 * 49) = 11 + 245 = 256.
Thus, the 50th term in the sequence is 256.
Regarding the type of reasoning used to solve this problem, we used inductive reasoning. Inductive reasoning involves observing patterns or examples and making generalizations or predictions based on those observations. In this case, we observed the pattern of adding 5 to the previous term and extended it to find the 50th term.
To find the rule that generates the sequence, we can observe the pattern between the terms. If we look closely, we can see that each term is obtained by adding 5 to the previous term.
Let's break it down step by step:
First term: -4
Second term: -4 + 5 = 1
Third term: 1 + 5 = 6
Fourth term: 6 + 5 = 11
So, the rule that generates this sequence is to add 5 to the previous term.
Now, to find the 50th term in the sequence, we can use the formula for arithmetic progression:
nth term = a + (n - 1) * d
Where:
a = first term of the sequence
n = term number we want to find
d = common difference between terms
In this case, the first term (a) is -4, and the common difference (d) is 5.
Let's substitute these values into the formula:
50th term = -4 + (50 - 1) * 5
= -4 + 49 * 5
= -4 + 245
= 241
Therefore, the 50th term in the sequence is 241.
Regarding the type of reasoning used to solve this problem, it is deductive reasoning. Deductive reasoning involves using specific observations or patterns to draw general conclusions or rules. In this case, by observing the pattern of the sequence, we deduced the rule that generates the terms.