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?
Each term adds 5 to the previous term.
The Nth term is 5N-9.
As for the reasoning method, review
http://www.socialresearchmethods.net/kb/dedind.php
To find the rule that generates the sequence, we need to identify the pattern or relationship between each term.
Looking at the sequence -4, 1, 6, 11, we can observe that each term is obtained by adding 5 to the previous term. So, the rule that generates this sequence can be expressed as:
n = n-1 + 5
where n represents the position of the term in the sequence.
To find the 50th term in the sequence, we can use this rule and substitute n = 50 into the equation:
n50 = n49 + 5
= (n48 + 5) + 5
= ((n47 + 5) + 5) + 5
= ...
Carrying out this calculation iteratively until we reach n1, we can find the 50th term. However, it is important to note that this method can become time-consuming for large numbers.
In terms of reasoning, the process used to identify the rule and find the 50th term in the sequence is based on inductive reasoning. This form of reasoning involves observing patterns in specific cases and making general conclusions or predictions based on those patterns. In this case, we observed the pattern of adding 5 to each term to obtain the next term and concluded that this pattern holds true for all terms in the sequence.