Answer:
Please check the explanation.
Step-by-step explanation:
Given the sequence
11, 13, 15, 17, 19, ...
Determining the Recursive formula:
We know that a recursive formula is termed as a formula that specifies each term of the given sequence using the preceding terms.
From the given sequence it is clear that every term can be obtained by adding two to the previous term.
i.e. 13 = 11+2, 15 = 13+2, 17 = 15+2, 19 = 17+2
so
aₙ₊₁ = aₙ+2, for n ≥1
Therefore, a recursive formula is:
Determining the Explicit formula:
Given the sequence
11, 13, 15, 17, 19, ...
An arithmetic sequence has a constant difference 'd' and is defined by

computing the differences of all the adjacent terms

The difference between all the adjacent terms is the same and equal to

also

so substituting
,
in the nth terms



Therefore, the Explicit formula is:

Answer:

Step-by-step explanation:
First, we change both denominators to the LCM (lowest common multiple) which is 8.

Since the denominators are the same, we can add the numerators.


or it can be written as

3/5 participate in after school sports...
of these, 1/2 play lacrosse......1/2 of 3/5..." of " means multiply..
1/2 * 3/5 = 3/10....so 3/10 play lacrosse