Questions: Barb is making a bead necklace. She strings 1 white bead, then 3 blue beads, then 1 white bead, and so on. Write the numbers for the first eight beads that are white. What is a rule for the pattern?

Barb is making a bead necklace. She strings 1 white bead, then 3 blue beads, then 1 white bead, and so on. Write the numbers for the first eight beads that are white. What is a rule for the pattern?
Transcript text: Barb is making a bead necklace. She strings 1 white bead, then 3 blue beads, then 1 white bead, and so on. Write the numbers for the first eight beads that are white. What is a rule for the pattern?
failed

Solution

failed
failed

Solution Steps

Step 1: Analyze the pattern

Barb strings beads in the following repeating sequence: 1 white bead, followed by 3 blue beads. This pattern repeats continuously. The sequence of beads can be represented as: \[ \text{White}, \text{Blue}, \text{Blue}, \text{Blue}, \text{White}, \text{Blue}, \text{Blue}, \text{Blue}, \dots \]

Step 2: Identify the positions of white beads

The white beads appear at the beginning of each repetition of the pattern. The positions of the first eight white beads are:

  1. Position 1 (1st bead)
  2. Position 5 (5th bead)
  3. Position 9 (9th bead)
  4. Position 13 (13th bead)
  5. Position 17 (17th bead)
  6. Position 21 (21st bead)
  7. Position 25 (25th bead)
  8. Position 29 (29th bead)
Step 3: Derive the rule for the pattern

The positions of the white beads follow an arithmetic sequence where each white bead is 4 positions apart. The rule for the \(n\)-th white bead's position is: \[ \text{Position of } n\text{-th white bead} = 4n - 3 \]

Final Answer

The positions of the first eight white beads are: \[ \boxed{1, 5, 9, 13, 17, 21, 25, 29} \] The rule for the pattern is: \[ \boxed{\text{Position of } n\text{-th white bead} = 4n - 3} \]

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Practice-RT2: Stacked Blocks-Number of Blocks Shown below are stacks of various blocks. All masses are given in the diagram in terms of M, the mass of the smallest block. Rank the total number of blocks in each stack. Explain your reasoning. Practice-RT3: Stacked Blocks-Average Mass Blocks are stacked on a table. Masses are given in terms of M, the mass of the smallest block.
failedAnswered
Which best describes the style and tone of the passage? neutral cynical sympathetic assertive
failedAnswered
Find dy/dx by implicit differentiation. tan^(-1)(3x^2y) = x + 4xy^2 dy/dx =
failedAnswered
How many atoms are shown in the image? Consider the simple cubic (primitive cube) unit cell shown in this image.
failedAnswered
Adames Corporation has two manufacturing departments-Cutting and Forming. The company used the following information at the beginning of the year to calculate predetermined overhead rates: - Estimated total direct labor-hours (DLHs): Cutting 6,000, Forming 23,000 - Estimated total machine-hours (MHs): Cutting 13,500, Forming 2,800 - Estimated total manufacturing overhead cost (fixed and variable): Cutting 732,000, Forming 247,000 During the most recent month, Adames started and completed one job. There were no beginning inventories. Information concerning the completed job is as follows: - Direct materials: Cutting 82,600, Forming 12,300 - Direct labor cost: Cutting 11,600, Forming 31,000 - Actual machine-hours: Cutting 1,700, Forming 140 - Actual direct labor-hours: Cutting 480, Forming 1,500 Assume that the company uses separate departmental predetermined overhead rates with the Cutting Dept using machine-hours as the allocation base and the Forming Dept using direct labor-hours. 1. Calculate the predetermined overhead rates for the Cutting and Forming departments separately (round to the nearest cent). 2. Using the departmental rates, calculate the total manufacturing overhead that would be applied to the job. 3. Calculate the cost per unit for the job if the job included 1,250 units (round to the nearest cent). 4. If the company had instead used one plantwide overhead rate, would you expect the job cost to be more or less accurate than what you calculated above?