Functions and Lines - Algebra

The sequence follows the pattern for the equation:

Therefore,

Lines can be written using the slope-intercept equation format:

Lines that are parallel have the same slope.

The given line has a slope of:

Only one of the choices also has the same slope and is the correct answer:

Lines can be written using the slope-intercept equation format:

Lines that are parallel have the same slope.

The given line has a slope of:

Only one of the choices also has the same slope and is the correct answer:

Lines can be written using the slope-intercept equation format:

Lines that are parallel have the same slope.

The given line has a slope of:

Only one of the choices also has the same slope and is the correct answer:

Lines can be written using the slope-intercept equation format:

Lines that are parallel have the same slope.

The given line has a slope of:

Only one of the choices also has the same slope and is the correct answer:

Lines can be written using the slope-intercept equation format:

Lines that are parallel have the same slope.

The given line has a slope of:

Only one of the choices also has the same slope and is the correct answer:

Lines can be written using the slope-intercept equation format:

Lines that are parallel have the same slope.

The given line has a slope of:

Only one of the choices also has the same slope and is the correct answer:

Lines can be written using the slope-intercept equation format:

Lines that are parallel have the same slope.

The given line has a slope of:

Only one of the choices also has the same slope and is the correct answer:

To evaluate substitute six in for every x in the equation.

To solve this problem replace every x in with .

Therefore,

If is one odd number, then the next odd number is . If their product is 143, then the following equation is true.

Distribute into the parenthesis.

Subtract 143 from both sides.

This can be solved by factoring, or by the quadratic equation. We will use the latter.

We are told that both integers are positive, so .

The other integer is .

The first term for the sequence is where . Thus,

So the first term is 4. Repeat the same thing for the second , third , fourth , and fifth terms.

We see that the first five terms in the sequence are

When finding consecutive numbers assign the first number a variable.

If the first number is assigned the letter n, then the second number that is consecutive must be and the third number must be .

Write it out as an equation and it should look like:

Simplify the equation then,

If then

And

So the answer is

Let the first number be .

If is an odd number, the next odd numbers will be:

, , , and

The fourth highest number would then be:

Set up an equation where the sum of all these numbers add up to .

Simplify this equation.

Subtract 20 from both sides.

Simplify both sides.

Divide by five on both sides.

Corresponding to the five numbers, the set of five consecutive numbers that add up to are:

The fourth largest number would be .

In each case, the terms increase by the same number, so all of these sequences are arithmetic.

Each term is the result of adding 1 to the previous term. 1 is the common difference.

Each term is the result of subtracting 1 from - or, equivalently, adding to - the previous term. is the common difference.

The common difference is 0 in a constant sequence such as this.

Each term is the result of adding to the previous term. is the common difference.

First, find the common difference for the sequence. Subtract the first term from the second term.

Subtract the second term from the third term.

To find the next value, add to the last given number.

In an arithmetic sequence the amount that the sequence grows or shrinks by on each successive term is the common difference. This is a fixed number you can get by subtracting the first term from the second.

So the sequence is adding 12 each time. Add 12 to 25 to get the third term.

So the unknown term is 37. To double check add 12 again to 37 and it should equal the fourth term, 49, which it does.

In each group of numbers, compare the difference of the second and first terms to that of the third and second terms. The group in which they are unequal is the correct choice.

The last group of numbers is the correct choice.

The common difference is the distance between each number in the sequence. Notice that each number is 3 away from the previous number.

What is the common difference in the following sequence?

Common differences are associated with arithematic sequences.

A common difference is the difference between consecutive numbers in an arithematic sequence. To find it, simply subtract the first term from the second term, or the second from the third, or so on...

See how each time we are adding 8 to get to the next term? This means our common difference is 8.