<p>All the positive even numbers are distributed into sets of the form:</p>
<p style="text-align: center">\[\{2\}, \{4, 6, 8\}, \{10, 12, 14, 16, 18\}, \{20, 22, 24, 26, 28, 30, 32\}, \dots\]</p>
<p>Find, in terms of \(r\), the</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">number of integers in the \(r^{\mathrm{th}}\) set; and</span></div></li><li><div class="list-item-content"><span class="list-item-text">the last integer in the \(r^{\mathrm{th}}\) set.</span></div></li></ol>
<p>Hence determine which set does the even integer \(2016\) belong to?</p>

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

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

number of integers in the \(r^{\mathrm{th}}\) set; and

the last integer in the \(r^{\mathrm{th}}\) set.

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

Arithmetic Progression

APGP

International Baccalaureate Higher Level Mathematics

Sets of APs

Sets of APs