document.write( "Question 1133165: 8;18;30:44\r
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Algebra.Com's Answer #750347 by MathLover1(20850) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( " $\"8\"$ , $\"18\"$ , $\"30\"$ , $\"44\"$ -> find differences first\r
\n" ); document.write( "\n" ); document.write( " $\"8\"$ ......... $\"18\"$ .......... $\"30\"$ .......... $\"44\"$
\n" ); document.write( "..... $\"10\"$ ......... $\"12\"$ ........... $\"14\"$ \r
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\n" ); document.write( "\n" ); document.write( "The pattern goes + $\"10\"$ , + $\"12\"$ , + $\"14\"$ , ...\r
\n" ); document.write( "\n" ); document.write( "Since the second difference is always + $\"2\"$ , the nth term must involve $\"n%5E2\"$ .\r
\n" ); document.write( "\n" ); document.write( "So let's say the nth number in the sequence = $\"n%5E2+%2B+an+%2B+b\"$ \r
\n" ); document.write( "\n" ); document.write( "To find $\"b\"$ , you can substitute in $\"n=0\"$ , i.e. what is the \"zeroth\" number in the sequence? In other words, what number would have come before $\"8\"$ ?\r
\n" ); document.write( "\n" ); document.write( "This number must have been $\"0\"$ , in order to continue the pattern of + $\"8\"$ , + $\"10\"$ , + $\"12\"$ , + $\"14\"$ , ...\r
\n" ); document.write( "\n" ); document.write( "So we now know the nth number = $\"n%5E2+%2B+an\"$ \r
\n" ); document.write( "\n" ); document.write( "Now just plug in any other value we know, to find the value of $\"+a\"$ . For example, using the first number in the sequence ( $\"n=1\"$ ), we get:
\n" ); document.write( " $\"1+%2B+a+=+8\"$
\n" ); document.write( " $\"a+=+7\"$ \r
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\n" ); document.write( "\n" ); document.write( "Therefore the nth term in this sequence is: $\"n%5E2+%2B+7n+\"$ \r
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