document.write( "Question 1116129: Find the first five terms in sequences with the following nth terms\r
\n" ); document.write( "\n" ); document.write( "a.2n^2+2
\n" ); document.write( "b. 6n+2
\n" ); document.write( "c. 10n-3
\n" ); document.write( "d. 2n-1
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Algebra.Com's Answer #731056 by KMST(5328) $\"\"$ $\"About$

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What the question is asking is what is the value of each expression for $\"n=1\"$ , $\"n=2\"$ , $\"n=3\"$ , $\"n=4\"$ , and $\"n=5\"$ .
\n" ); document.write( "Plug in values for $\"n\"$ , and find the result of each formula given.
\n" ); document.write( "It is not rocket science.
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\n" ); document.write( "a. For the sequence whose terms are given by $\"2n%5E2%2B2\"$ ,
\n" ); document.write( "For $\"n=1\"$ , the (first) term is $\"2%2A1%5E2%2B2=2%2A1%2B2=2%2B2=4\"$ .
\n" ); document.write( "For $\"n=2\"$ , the (second) term is $\"2%2A2%5E2%2B2=2%2A4%2B2=8%2B2=10\"$ .
\n" ); document.write( "For $\"n=3\"$ , the (third) term is $\"2%2A3%5E2%2B2=2%2A9%2B2=18%2B2=20\"$ .
\n" ); document.write( "For $\"n=4\"$ , the (fourth) term is $\"2%2A4%5E2%2B2=2%2A16%2B2=32%2B2=34\"$ .
\n" ); document.write( "For $\"n=5\"$ , the (fifth) term is $\"2%2A5%5E2%2B2=2%2A25%2B2=50%2B2=62\"$ .
\n" ); document.write( "So, the first five terms are 4, 10, 20, 34, 62.
\n" ); document.write( "The expression $\"2n%5E2%2B2\"$ is a quadratic polynomial,
\n" ); document.write( "meaning a polynomial of degree 2.
\n" ); document.write( "As a function of $\"n\"$ that expression is a quadratic function.
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\n" ); document.write( "You can do the same for b, c, and d.
\n" ); document.write( "The expressions for b, c, and d are linear functions of $\"n\"$ .
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\n" ); document.write( "NOTE: The question was not difficult, so it must be leading to some conclusion.
\n" ); document.write( "If you calculate the differences between consecutive terms,
\n" ); document.write( "you will find that they are all the same for the terms given by
\n" ); document.write( "each of the linear expressions in b, c, and d.
\n" ); document.write( "If you calculate the differences between consecutive terms for the five terms
\n" ); document.write( "4, 10, 20, 34, and 62, given by the quadratic expression $\"2n%5E2%2B2\"$ ,
\n" ); document.write( "you find that the \"first differences\" are 6, 10, 14, and 18:
\n" ); document.write( " $\"10-4=6\"$ , $\"20-10=10\"$ , $\"34-20=14\"$ , and $\"62-34=18\"$ .
\n" ); document.write( "If you calculate the differences of the differences (the \"second differences\"),
\n" ); document.write( "you find:
\n" ); document.write( " $\"10-6=4\"$ , $\"14-10=4\"$ , $\"18-14=4\"$ .
\n" ); document.write( "For linear sequences, the first differences are the same.
\n" ); document.write( "For quadratic sequences, the second differences are the same.
\n" ); document.write( "That is probably where your teacher is going with this question.\r
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