document.write( "Question 120780: Using the following sequence,determine what type of function describes the sequence. Once you determine the type of function,find the function algebraically.(4,9,17,28,42,59,...) \n" ); document.write( "
Algebra.Com's Answer #88560 by Fombitz(32388)\"\" \"About 
You can put this solution on YOUR website!
Let's look at each consecutive pair and how you get from the first number to the second number.
\n" ); document.write( "4-9: +5
\n" ); document.write( "9-17: +8
\n" ); document.write( "17-28: +11
\n" ); document.write( "28-42: +14
\n" ); document.write( "42-59: +17
\n" ); document.write( "Looks like you add 3 to the difference from the previous pair.
\n" ); document.write( "The next pair would look like this,
\n" ); document.write( "59-?: +20
\n" ); document.write( "59+20=79.
\n" ); document.write( "The next number is 79.
\n" ); document.write( "Now the pattern.
\n" ); document.write( "4-9: 5= 1*5
\n" ); document.write( "4-17: 13 = 5 + (5+3) = 2*5 + 3
\n" ); document.write( "4-28: 24 = 5 + (5+3) + (5+3+3) = 3*5 + 3*3
\n" ); document.write( "4-42: 38 = 5 + (5+3) + (5+3+3) + (5+3+3+3)=4*5+6*3
\n" ); document.write( "4-59: 55 = 5 + (5+3) + (5+3+3) + (5+3+3+3) + (5+3+3+3+3) =5*5+10*3
\n" ); document.write( "4-79: 66 = 5 + (5+3) + (5+3+3) + (5+3+3+3) + (5+3+3+3+3) + (5+3+3+3+3+3)=6*5+15*3
\n" ); document.write( "The formula for the nth term would look like
\n" ); document.write( "\"a%5Bn%5D=4%2B%28n-1%29%2A5+%2B++3%2Asum%28+n-1%2C+0%2C+n-1+%29\"
\n" ); document.write( "You can simplify the sum term since
\n" ); document.write( "\"sum%28+n-1%2C+0%2C+n-1+%29=%28%28n-1%29%28n-2%29%29%2F2\"
\n" ); document.write( "Since we have n-2, this simplification only applies for n>1.
\n" ); document.write( "For n=1, the sum equals zero.
\n" ); document.write( "\"a%5B1%5D=4%2B%281-1%29%2A5+%2B++0\"
\n" ); document.write( "\"a%5B1%5D=4\"
\n" ); document.write( "Therefore
\n" ); document.write( "\"a%5Bn%5D=4%2B%28n-1%29%2A5+%2B++3%2A%28%28n-1%29%28n-2%29%29%2F2\"
\n" ); document.write( "\"a%5Bn%5D=4%2B%28n-1%29%2A%285+%2B++3%2A%28n-2%29%2F2%29\" for n>1
\n" ); document.write( "and
\n" ); document.write( "\"a%5B1%5D=4\"
\n" ); document.write( "Check the answer with a couple of points to make sure everything looks good.
\n" ); document.write( "2nd term : n=2
\n" ); document.write( "\"a%5Bn%5D=4%2B%28n-1%29%2A%285+%2B++3%2A%28n-2%29%2F2%29\"
\n" ); document.write( "\"a%5Bn%5D=4%2B%282-1%29%2A%285+%2B++3%2A%282-2%29%2F2%29\"
\n" ); document.write( "\"a%5Bn%5D=4%2B%281%29%2A%285%29\"
\n" ); document.write( "\"a%5B2%5D=9\"
\n" ); document.write( "5th term : n=5
\n" ); document.write( "\"a%5Bn%5D=4%2B%28n-1%29%2A%285+%2B++3%2A%285-2%29%2F2%29\"
\n" ); document.write( "\"a%5B5%5D=4%2B%284%29%2A%285+%2B++3%2A%283%29%2F2%29\"
\n" ); document.write( "\"a%5B5%5D=4%2B%284%29%2A%2819%2F2%29\"
\n" ); document.write( "\"a%5B5%5D=4%2B%2838%29\"
\n" ); document.write( "\"a%5B5%5D=42\"
\n" ); document.write( "The asnwers check out to the originals. \n" ); document.write( "
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