Mathematics

Question

A pile of newspaper was 17 3/4 inches high. Each consecutive week for the next 5 weeks the height of pile increase by 8 7/12 inches. What is the height in inches, of the pile after 3 weeks?

1 Answer

  • Answer: the height in inches, of the pile after 3 weeks is 34 11/12 inches

    Step-by-step explanation:

    Each consecutive week for the next 5 weeks the height of pile increase by 8 7/12 inches. Converting 8 7/12 inches to improper fraction, it becomes 103/12 inches. The height is increasing in an arithmetic progression. The formula for determining the nth term of an arithmetic sequence is expressed as

    Tn = a + (n - 1)d

    Where

    a represents the first term of the sequence.

    d represents the common difference.

    n represents the number of terms in the sequence.

    From the information given,

    a = 17 3/4= 71/4 inches

    d = 103/12 inches

    n = 3 weeks

    the height in inches, of the pile after 3 weeks, T3. Therefore,

    T3 = 71/4 + (3 - 1)103/12

    T3 = 71/4 + 2 × 103/12 = 71/4 + 103/6

    T3 = 419/12 inches = 34 11/12 inches

NEWS TODAY