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A pattern of dots is shown below. Determine the formula for the number of dots in term N and draw the patterns for the next three terms.

Mathematics

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Step-by-step solution

3 steps
  1. Analyze the pattern of dots.

    The given pattern shows:

    • Term 0: 0 dots
    • Term 1: 2 dots (arranged as one pair)
    • Term 2: 4 dots (arranged as two pairs)
    • Term 3: 6 dots (arranged as three pairs) The number of dots in each term is twice the term number. This can be represented by the formula 2N2N, where NN is the term number.
  2. Calculate the number of dots for the next three terms.

    The next three terms are Term 4, Term 5, and Term 6.

    • For Term 4: 2×4=82 \times 4 = 8 dots.
    • For Term 5: 2×5=102 \times 5 = 10 dots.
    • For Term 6: 2×6=122 \times 6 = 12 dots.
  3. Draw the patterns for Term 4, Term 5, and Term 6, following the arrangement of horizontal pairs of dots stacked vertically.

    a) The next three terms are:

    Term 4:
    o o
    o o
    o o
    o o

    Term 5:
    o o
    o o
    o o
    o o
    o o

    Term 6:
    o o
    o o
    o o
    o o
    o o
    o o

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