An arithmetic sequence is represented in the following table. enter the
missing term of the sequence.
1 2 3 4 26
y -103 -94 -85 -76 ?

122

Step-by-step explanation:

An arithmetic sequence means a number is added each term.  There is a term for where a number is multiplied as well.  But in this case the first number is -103, the second number is -94 and the third number is -85.  Can you tell what number is added each time?

The number is 9.  -103+9=-94 and -94+9=-85 and so on.  Now we want a way to find the term way further down the line.

Think of it doing it all at once.  -103+9+9 gets us the third term right?  so that's 2*9.  -103+3*9 would get us the fourth.  Hopefully that makes sense, but let me know if it doesn't.  But for a few more examples, if we want the fifth term we would do -103+4*9 and getting the tenth would need -103+9*9.  So basically we take the number term we want (in this case we want the 26th) and then take -103+ n*9, where n is the term we want minus 1, or in this case 25.  so that's -103+25*9

Let me know if you need more of an explanation.

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.