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Question

$left curly bracket n open parentheses n plus 1 close parentheses open parentheses 2 n plus 1 close parentheses colon n element of Z right curly bracket subset of$

(a) ${6 k : k \in Z}$
${12 k : k \in Z}$
${18 k : k \in Z}$
${24 k : k \in Z}$

The correct answer is: (a) $left curly bracket 6 k blank colon k element of Z right curly bracket$

Let $A equals left curly bracket n open parentheses n plus 1 close parentheses open parentheses 2 n plus 1 close parentheses colon n element of Z right curly bracket$
Putting $n equals plus-or-minus 1 comma blank plus-or-minus 2 comma blank horizontal ellipsis. comma$ we get $A equals left curly bracket horizontal ellipsis minus 30 comma blank minus 6 comma blank 0 comma blank 6 comma blank 30 comma blank horizontal ellipsis right curly bracket$
$rightwards double arrow open curly brackets n open parentheses n plus 1 close parentheses open parentheses 2 n plus 1 close parentheses colon n element of Z close curly brackets subset of left curly bracket 6 k colon k element of Z right curly bracket$

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