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?
To find the rule that generates the sequence, you need to observe the pattern in the numbers and identify the relationship between them. In this sequence, the numbers increase by 5 at each step. Therefore, the rule for generating this sequence is adding 5 to the previous term.
Using this rule, we can find the 50th term in the sequence. To calculate the 50th term, you start with the first term (-4) and add 5 to it 49 times.
Formula to find the nth term in an arithmetic sequence:
nth term = a + (n - 1)d
In this case:
a = -4 (the first term)
d = 5 (common difference)
Plugging these values into the formula, we can calculate the 50th term:
50th term = -4 + (50 - 1)*5
= -4 + 49*5
= -4 + 245
= 241
Therefore, the 50th term in the sequence is 241.
When solving this problem, you are using inductive reasoning. Inductive reasoning involves making generalizations based on a pattern observed in specific cases. In this case, you are identifying the pattern in the given terms and using it to make predictions about the sequence as a whole.