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Mathematics

1 answer:

gayaneshka [121]3 years ago

8 0

Answer:

Real numbers are Closed under multiplication.

Irrational numbers are Not Closed under division.

Integers are Closed under subtraction.

Positive rational numbers are Closed under addition.

Step-by-step explanation:

a) The product of any two real numbers is a real number, so the set is closed.

b) In some cases, the quotient may be rational. (√18)/(√2) = 3, for example. So, the set is not closed.

c) The difference of any two integers is an integer, so the set is closed.

d) The sum of any two positive rational numbers is a postive rational number, so the set is closed.

Sorry if its out of order but i hope it helps enough

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Write an explicit formula for an, the nth term of the sequence 112, -28, 7, ....

MA_775_DIABLO [31]

Answer:

$a_n=112\left(-\frac{1}{4}\right)^{n-1}$

Step-by-step explanation:

<u>Geometric Sequences</u>

There are two basic types of sequences: arithmetic and geometric. The arithmetic sequences can be recognized because each term is found as the previous term plus a fixed number called the common difference.

In the geometric sequences, each term is found by multiplying (or dividing) the previous term by a fixed number, called the common ratio.

We are given the sequence:

112, -28, 7, ...

It's easy to find out this is a geometric sequence because the signs of the terms are alternating. If it was an arithmetic sequence, the third term should be negative like the second term.

Let's find the common ratio by dividing each term by the previous term:

$\displaystyle r=\frac{-28}{112}=-\frac{1}{4}$