Arithmetic Sequences and Expressions

The video tutorial covers three main problems. First, it solves for 2xy using two equations with variables x and y in terms of a and b. Next, it addresses a geometry problem involving a rectangular circuit board, relating its width, perimeter, and area. Finally, it explores arithmetic sequences, examining transformations and determining which sequences remain arithmetic.

If x + y = a and x - y = b, what is the expression for x in terms of a and b?

• x = (a - b) / 2

• x = a * b

• x = (a + b) / 2

• x = a / b

What is the expression for y in terms of a and b if x + y = a and x - y = b?

• y = a * b

• y = a / b

• y = (a - b) / 2

• y = (a + b) / 2

What is the value of 2xy if x + y = a and x - y = b?

• a^2 + b^2

• a^2 - b^2

• 2(a^2 - b^2)

• a^2 / b^2

In the circuit board problem, what is the expression for the height in terms of perimeter and width?

• height = p / 2 + w

• height = p - 2w

• height = p / 2 - w

• height = 2p - w

What is the equation derived for the area of the circuit board in terms of width and perimeter?

• k = pw + w^2

• k = pw - w^2

• k = 2pw - w^2

• k = pw / 2 - w^2

Which of the following is the correct final equation for the circuit board problem?

• 2w^2 - pw + 2k = 0

• 2w^2 + pw - 2k = 0

• w^2 + pw - 2k = 0

• w^2 - pw + 2k = 0

In an arithmetic sequence, what is the common difference if the sequence is p, r, s, t, u?

• All of the above

• t - s

• s - r

• r - p

If each term of an arithmetic sequence is multiplied by 2, what happens to the sequence?

• It becomes a geometric sequence

• It remains an arithmetic sequence

• It becomes a quadratic sequence

• It becomes a constant sequence

What happens to an arithmetic sequence if each term is decreased by 3?

• It becomes a quadratic sequence

• It remains an arithmetic sequence

• It becomes a constant sequence

• It becomes a geometric sequence

If each term of an arithmetic sequence is squared, what happens to the sequence?

• It becomes a constant sequence

• It remains an arithmetic sequence

• It becomes a geometric sequence

• It becomes a quadratic sequence