The following sequences' first ten terms should be given. Assume that the sequences are in base 2 and have an index of 1.Indicate whether the sequence is increasing, decreasing, non-increasing, or non-decreasing.1) The nth term is the largest integer k such that&nbsp;k!≤n.2) The nth term is 1/n.3) The nth term is 3.4) The nth term is&nbsp;n2.5) The nth term is [log⁡n].

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The following sequences&#039; first ten terms should be given. Assume that the sequences are in base 2 and have an index of 1.Indicate whether the sequence is increasing, decreasing, non-increasing, or non-decreasing.1) The nth term is the largest integer k such that&amp;nbsp;k!≤n.2) The nth term is 1/n.3) The nth term is 3.4) The nth term is&amp;nbsp;n2.5) The nth term is [log⁡n].

Dominique Green · Accepted Answer

1) The nth term is the largest integer k such that k!≤n.     First term n=1⇒1!≤1    n=2⇒2!≤2    n=3⇒2!≤3, 3≠6    n=4⇒2!≤4    n=5⇒2!≤5    n=6⇒3!≤6    n=7⇒3!≤7, 4≠24    n=8⇒3!&amp;lt;8    n=9⇒3!&amp;lt;9    n=10⇒3!&amp;lt;10    So, first terms are 1,2,2,2,2,3,3,3,3,3    Its

portafilses · Accepted Answer

3) The nth term is 3.&amp;lt;an≥&amp;lt;3&amp;gt;Sequence is always the same.First ten are &amp;lt;3,3,3,3,3,3,3,3,3,3&amp;gt; - non-decreasing and non-increasing5) The nth term is [log⁡n]It&#039;s ceiling functionlog⁡1=0log22=12&amp;lt;log25&amp;lt;32&amp;lt;log⁡7&amp;lt;33&amp;lt;log⁡9&amp;lt;41&amp;lt;log23&amp;lt;2log24=22&amp;lt;log⁡6&amp;lt;3log⁡8=33&amp;lt;log⁡10&amp;lt;4Thus,&amp;nbsp;&amp;lt;an≥[log⁡n]First ten terms are&amp;nbsp;&amp;lt;0,1,2,2,3,3,3,3,4,4&amp;gt;Non-decreasing

Give the first ten terms of the following sequences. Assume that the sequences start with an index o

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