document.write( "Question 1127336: n : 1st term, 2nd term, 3rd term, 4th term, 5th term, 6th term, ………. 15th term
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\n" ); document.write( "\n" ); document.write( "Find the 15th term. HINT: I think we need to multiply the series by 2 and then find factors and then solve. I am getting stuck between 4th and 5th term to find meaningful series for factors. Could you please help solve ? \n" ); document.write( "
Algebra.Com's Answer #743735 by math_helper(2461)\"\" \"About 
You can put this solution on YOUR website!

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document.write( "     Term         Diff       
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document.write( "\"+a%5B1%5D+=+-3+\"
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document.write( "\"+a%5B2%5D+=+0+\"              3
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document.write( "\"+a%5B3%5D+=+4+\"              4    
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document.write( "\"+a%5B4%5D+=+9+\"              5         
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document.write( "\"+a%5B5%5D+=+15+\"             6  
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document.write( "\"+a%5B2%5D+=+a%5B1%5D+%2B+3+\"
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document.write( "\"+a%5B3%5D+=+a%5B2%5D+%2B+4+=+%28a%5B1%5D%2B3%29+%2B+4+\"
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document.write( "\"+a%5B4%5D+=+a%5B3%5D+%2B+5+=+%28a%5B2%5D+%2B+4%29+%2B+5+=+%28a%5B1%5D%2B3%29%2B4%2B5+\" 
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document.write( "The pattern is:
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document.write( "\"++a%5Bn%5D+=+a%5B1%5D+%2B+3%2B4%2B5+\" + . . .  + \"+%28n%2B1%29+\" 
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document.write( "If we write it a little differently:
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document.write( "\"++a%5Bn%5D+=+a%5B1%5D+\" +  (1+2+3 + . . . +  (n+1)) - 3 
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document.write( "[ Then noting the sum of the first m integers: (1+2+ . . . + m )  =   (m)(m+1)/2  ] 
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document.write( "we can simplify:
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document.write( "\"++a%5Bn%5D+=+a%5B1%5D+\" +  \"+%28%28n%2B1%29%28n%2B2%29%29%2F2+\" - 3 
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document.write( "Combining \"+a%5B1%5D+=+-3+\" with the -3 we introduced :
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document.write( "\"+blue+%28++a%5Bn%5D+=+-6+%2B+%28%28n%2B1%29%28n%2B2%29%29%2F2+%29+\"    n=1,2,3, . . . 
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document.write( "Check with given values:
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document.write( "a[1] = -6 + (2)(3)/2 = -6 + 3 = -3
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document.write( "a[2] = -6 + (3)(4)/2 = -6 + 6 = 0
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document.write( "a[3] = -6 + (4)(5)/2 = -6 + 10 = 4

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document.write( "You can plug in n=15 to find a[15] = 130.\r
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