等差数列
对任意的k∈N*，<span class="equation-text" data-index="0" data-equation="a_1" contenteditable="false"><span></span><span></span></span>+<span class="equation-text" data-index="1" data-equation="a_n" contenteditable="false"><span></span><span></span></span>=<span class="equation-text" data-index="2" data-equation="a_2" contenteditable="false"><span></span><span></span></span>+<span class="equation-text" data-index="3" data-equation="a_{n-1}" contenteditable="false"><span></span><span></span></span>=<span class="equation-text" data-index="4" data-equation="a_3" contenteditable="false"><span></span><span></span></span>+<span class="equation-text" data-index="5" data-equation="a_{n-2}" contenteditable="false"><span></span><span></span></span>=…=<span class="equation-text" data-index="6" data-equation="a_k" contenteditable="false"><span></span><span></span></span>+<span class="equation-text" contenteditable="false" data-index="7" data-equation="a_{n-k+1}"><span></span><span></span></span>。
对任意的k∈N*，有<span class="equation-text" data-index="0" data-equation="s_k" contenteditable="false"><span></span><span></span></span>，<span class="equation-text" data-index="1" data-equation="s_{2k}" contenteditable="false"><span></span><span></span></span>-<span class="equation-text" contenteditable="false" data-index="2" data-equation="s_k"><span></span><span></span></span>，<span class="equation-text" data-index="3" data-equation="s_{3k}"><span></span><span></span></span>-<span class="equation-text" data-index="4" data-equation="s_{2k}"><span></span><span></span></span>，…，<span class="equation-text" data-index="5" data-equation="s_{nk}"><span></span><span></span></span>-<span class="equation-text" data-index="6" data-equation="s_{(n-1)k}"><span></span><span></span></span>…成等差数列。
等比数列
对任意的k∈N*，<span class="equation-text" data-index="0" data-equation="a_1" contenteditable="false"><span></span><span></span></span><span class="equation-text" data-index="1" data-equation="a_n" contenteditable="false"><span></span><span></span></span>=<span class="equation-text" data-index="2" data-equation="a_2" contenteditable="false"><span></span><span></span></span><span class="equation-text" data-index="3" data-equation="a_{n-1}" contenteditable="false"><span></span><span></span></span>=<span class="equation-text" data-index="4" data-equation="a_3" contenteditable="false"><span></span><span></span></span><span class="equation-text" data-index="5" data-equation="a_{n-2}" contenteditable="false"><span></span><span></span></span>=…=<span class="equation-text" data-index="6" data-equation="a_k" contenteditable="false"><span></span><span></span></span><span class="equation-text" contenteditable="false" data-index="7" data-equation="a_{n-k+1}"><span></span><span></span></span>。
任意两项<span class="equation-text" data-index="0" data-equation="a_m" contenteditable="false"><span></span><span></span></span>，<span class="equation-text" contenteditable="false" data-index="1" data-equation="a_n"><span></span><span></span></span>的关系为<span class="equation-text" data-index="2" data-equation="a_n"><span></span><span></span></span>=<span class="equation-text" data-index="3" data-equation="{{a_m}q^{n-m}}"><span></span></span>
