Question

The first three terms of an arithmetic sequence are given by x, (2x -5), and 8.6.

Answer 1

What is the first term and the common difference?

Answer 2

Well the differnce is "common" for a reason.
Set the difference equal, solve for x, and you have your answers.

Answer 3

a, b, c

common diff = c-b or b-a

Answer 4

What is the reasoning for (2x - 5) - x = 8.6 - (2x - 5)

Answer 5

Why do we make them equal

Answer 6

FOO FOO STEAL MAH MEDAL

Answer 7

Because we know in an arithmeic series, that each term has the same difference as the preveious

Answer 8

It's actually by definition.

Answer 9

I understand that they equal, d is equal to d but why can't I just go 2x - 5 - x = the answer?

Answer 10

Because. That doesn't simplify to a constant.

Answer 11

Is it because you require an equation to solve the problem and not an expression?

Answer 12

Yes.

Answer 13

it's correct.

Answer 14

It's because you get two expressions, actually. Those two expressions are equal, but not equivalent.

Answer 15

But 2x - 5 - x would be x - 5 which is just an expression right? but we need an equation to solve the problem? I am trying to understand the philosophy behind how this works.

Answer 16

(in the sense that x+3+8 is equivalent to x+2+9)

Answer 17

if you think,

a-b = b-c

both will give you the same value.

Answer 18

Well. We actually get two expressions.

Answer 19

a-b = b-c, as foo foo said.

Answer 20

We do but the expressions equal eachother right?

Answer 21

yes.

Answer 22

we will get a value for 'x' then.

Answer 23

a-b is an expression, and b-c is also an expression. Each of these is the comon difference.

Answer 24

(2x - 5) - x = x - 5 you CAN'T make it equal to zero right?

Answer 25

Wat do you mean, equal zero?

Answer 26

No, not equal to zero

Answer 27

Like if you went 2x -5 - x = x -5 then took

x - 5 = 0, x = 5

Answer 28

Because x-5 is the common difference.

Answer 29

not zero; the common diference

Answer 30

(2x - 5) - x = 8.6 - (2x - 5)
x = 6.2

Answer 31

I see
But making a quadratic equal 0 works because it when you make a quadratic equal to 0 it finds the x intercepts right?

Answer 32

We know a value x-5 is the common difference, and also a value 2x-5-x, which is also the common difference.
We can set them equal because we know the represent the same value (the common difference)

Answer 33

Well, you set it equal to zero

Answer 34

because in a quadratic function y=ax^2+bx+c, you are looking for the x-value when y is equal to zero (in other words, the x intercept)

Answer 35

the point (x,0) is the x intercept.

Answer 36

Another question, adding a negative is the same as minusing a positive and minusing a postive is the same as adding a negative right?

Answer 37

There are two unknowns in a quadratic function.

Answer 38

Thanks

Answer 39

When we search for the x-intercept, we know that y=0, because the x intercept is on the x-axis and has no vertical height.

Answer 40

Another question, adding a negative is the same as minusing a positive and minusing a postive is the same as adding a negative right?
- those are properties the directly follow from our definition of negative numbers and subtraction, as well as addition.