Identify the number that does not belong with the other three. explain your reasoning. negative 10 over 2, negative 13.4, square root 18, 22.7 repeating 7

√18

Step-by-step explanation:

The numbers in the list are:

-10/2  

-13.4

√18

22.777

First, let's define two groups:

Rational numbers: Are those with a finite number of decimals after the decimal point, or with a pattern that repeats infinitely after the decimal point (like in the 22.77... with the 7 repeatings)

These types of numbers can be written as the quotient of two integer numbers.

Irrational numbers: Have infinite decimals after the decimal point and there is no pattern at all, they can not be written as the quotient between two integer numbers. Square roots of numbers that are not perfect squares (the solution is an integer) are irrational numbers.

Here, with that definition, we can see that: -10/2, -13.4 and 22.77...

are rational numbers, now let's see √18

We know that 4*4 = 16, and 5*5 = 25

so there are no integer X such x*x = 18

Then √18 is an irrational number and is the one that does not belong in the list.

the first sequence is an arithmetic sequence.