<p>From merely the first few terms, it is impossible to know all the terms of a sequence. For example, a sequence whose first five terms are \(1, 2, 3, 4, 5\) could be</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">the sequence of all positive integers; or</span></div></li><li><div class="list-item-content"><span class="list-item-text">the sequence \(1, 2, 3, 4, 5, 0, 0, 0, \dots\) whose first five terms are \(1, 2, 3, 4, 5\) but the rest of the terms are all \(0\)'s.</span></div></li></ol>

From merely the first few terms, it is impossible to know all the terms of a sequence. For example, a sequence whose first five terms are \(1, 2, 3, 4, 5\) could be

the sequence of all positive integers; or

the sequence \(1, 2, 3, 4, 5, 0, 0, 0, \dots\) whose first five terms are \(1, 2, 3, 4, 5\) but the rest of the terms are all \(0\)'s.

APGP

International Baccalaureate Higher Level Mathematics