Maths-
General
Easy

Question


A project coordinator at a banquet hall is given the task of arranging seating for an awards ceremony. The figure above shows the first three possible arrangements of tables and the maximum number of seats in each arrangement. If the number of seats in each successive arrangement is increased by 6 over the preceding arrangement, which of the following represents the maximum number of seats around n tables?

  1. 6n
  2. 2(3n + 1)
  3. 6(n + 1)
  4. 6(n + 3)

The correct answer is: 2(3n + 1)


    HINT: From the arrangements provided, find the appropriate sequence and hence we get the equation.
    Complete step by step solution:
    From Arrangement Ⅰ, maximum number of seats = 8
    From Arrangement Ⅱ, maximum number of seats = 14
    From Arrangement Ⅲ, maximum number of seats = 20
    Here we get an arithmetic sequence with numbers 8, 14, 20….
    We know that the formula of Arithmetic progression is an = a1 + (n - 1)d,
    Where, an is the nth term in the sequence, a1 is the first term and d is the common difference.
    On substituting the values in the formula, we get an = 8 + (n - 1)6 = 6n + 2
    This can be written as 2(3n + 1).
    So, 2(3n + 1) represents the maximum number of seats around n tables.
    Hence option B is the correct answer.

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