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Sets of APs

Sets of APs

IB Year 5 | Grade 11

All the positive even numbers are distributed into sets of the form:

\[\{2\}, \{4, 6, 8\}, \{10, 12, 14, 16, 18\}, \{20, 22, 24, 26, 28, 30, 32\}, \dots\]

Find, in terms of \(r\), the

  1. number of integers in the \(r^{\mathrm{th}}\) set; and
  2. the last integer in the \(r^{\mathrm{th}}\) set.

Hence determine which set does the even integer \(2016\) belong to?

Solution:

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Answer:(i) \(2r-1\) integers (ii) Last integer \(2r^2\) \(2016\) belongs to the \(32\)nd set.

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