Arithmetic Sequences Explicit and Recursive and Linear Equations

There are 30 rows in a corner section of an arena. Each row contains 3 more seats than the row in front of it. If there are 15 seats in the first row, 18 seats in the second row, 21 seats in the third row, etc., which equation(s) represents the number of seats s in the nth row? Select all that apply.

• s(1) = 12, s(n+1) = s(n) +3

• s(1) = 15, s(n+ 1) = s(n) + 3

• s(1) = 30, s(n+ 1) = s(n) + 3

• s(n) = 12 + 3n

• s(n) = 15 + 3n

The recursive formula for an arithmetic sequence has the form f(n + 1) = f(n) + d; f(0) = a.

What does 'd' represent? Select all that apply.

• the common difference

• the y-intercept

• the value of the first term

• the slope

• f(0)

The recursive formula for an arithmetic sequence has the form f(n + 1) = f(n) + d; f(0) = a.

What does 'a' represent? Select all that apply.

• the common difference

• f(0)

• y-intercept

• the value of the first term

• f(1)

The recursive formula for an arithmetic sequence has the form f(n + 1) = f(n) + d; f(0) = a.

What does 'a + d' represent? Select all that apply.

• the common difference

• f(1)

• the y-intercept

• the slope

• the value of the first term

This arithmetic sequence is defined by the function f(n).

9, 13, 17, 21, 25, .....

What is the y-intercept of this function?

-5, -2, 1, 4, 7, 10,......

Which Next-Now statement matches the sequence?

• Next = Now - 3

• Next = Now - 5

• Next = Now + 3

• Next = Now + 5

What is the Next-Now equation for the arithmetic sequence whose common difference is d, where d is a rational number?

• Next = Now + d

• Next = Now - d

• Next = Now × d

• Next = Now ÷ d

The equation y = 5x + 3 is a linear model for an arithmetic sequence. Which recursive function is a model for the same sequence

• f(n + 1) = f(n + 3); f(0) = 5

• f(n + 1) = f(n + 5) + 3; f(0) = 1

• f(n + 1) = f(n) + 5; f(0) = 3

• f(n + 1) = f(n) + 3; f(0) = 5

The recursive formula for an arithmetic sequence is f(n + 1) = f(n) + 7; f(0) = 3. Which equations are linear models for this sequence? Select all that apply.

• y= 3x + 7

• f(n) = 3n + 7

• f(n) = 7n + 3

• y = 7x + 3

• f(n + 1) = 7⋅f(n) + 3

Write a recursive rule for the sequence 17, 1, -15, -31 . . .

• a_n = a_n-1 + 16

• a_n = a_n-1 - 17

• a_n = a_n-1 - 15

• a_n = a_n-1 - 16