Making Explicit and Recursive Formulas

Write an explicit equation and a recursive equation to represent the sequence.

A sequence is given by the explicit formula below, where n represents the term number. Write the first 5 terms in the sequence.

• 6, 4, 2, 0, -2, ...

• -2, 4, 10, 16, 22, ...

• 4, 2, 0, -2, -4, ...

• 4, 10, 16, 22, 28, ...

Which recursive formula represents the sequence?

Karie is making a quilt with a design of rectangles. The largest rectangle has a length of 60 inches. Rectangle 2 is located inside the first rectangle, with a side length 75% the length of Rectangle 1. The pattern continues like this using the 75% reduction factor. Which rectangle will first have a length of less than 20 inches?

• Rectangle 3

• Rectangle 4

• Rectangle 5

• Rectangle 6

Which statement is true about this formula?

• It is an EXPLICIT formula. The first four terms are 5,7,9,11

• It is a RECURSIVE formula. The first four terms are 5,13,29,61

• It is an EXPLICIT formula. The first four terms are 13,15,17,19

• It is a RECURSIVE formula. The first four terms are 13,29,61,125

Write a recursive formula for the following sequence: 1, -3, 9, -27,...

• a₁= 1

  a_n= (a_n-1)(-3)

• a₁= 1

  a_n= a_n-1 -4

• a₁= -3

  a_n= (a_n-1)(-3)

• a₁= 1

  a_n= (a_n)(-3)

• A

• B

• C

• None of these

For the sequence, write a recursive formula. a₁ = 24, a₂ = 18, a₃ = 12, a₄  = 6, a₅ = 0, …

• a_n = a_n-1 - 6

• a_n = a_n-1 + 24

• g_n = -6 · g_n-1

• g_n = 24 · g_n-1

Given the recursive formula below, find the first five terms. u_1 = 3 u_n = u_{n-1} + 2

• 3, 5, 7, 9, 11

• 5, 7, 9, 11, 13

Given the first five terms, write the recursive formula.
15, 12, 9, 6, 3 ....

• u₁ = 15
  u_n = u_n-1 + 3

• u₀ = 15
  u_n = u_n-1 + 3

• u₁ = 15
  u_n = u_n-1 - 3 

• u₀ = 15
  u_n = u_n-1 - 3