document.write( "Question 472775: What are the next two terms of this sequence?\r
\n" ); document.write( "\n" ); document.write( "-21, -9, 11, 39\r
\n" ); document.write( "\n" ); document.write( "Thanks!!! \n" ); document.write( "

Algebra.Com's Answer #324131 by Theo(13342) $\"\"$ $\"About$

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-21, -9, 11, 39
\n" ); document.write( "it appears that the formula for this would be:
\n" ); document.write( "a[1] = -21
\n" ); document.write( "a[n] = a[n-1] + 12 + 8*(n-2)
\n" ); document.write( "we start with:
\n" ); document.write( "a[1] = -21
\n" ); document.write( "a[2] = -21 + 12 + 8*0 = -21 + 12 = -9
\n" ); document.write( "a[3] = -9 + 12 + 8*1 = -9 + 12 + 8 = -9 + 20 = 11
\n" ); document.write( "a[4] = 11 + 12 + 8*2 = 11 + 12 + 16 = 39
\n" ); document.write( "this would make:
\n" ); document.write( "a[5] = 39 + 12 + 8*3 = 39 + 12 + 24 = 75
\n" ); document.write( "if this formula is correct, then the next number in the sequence is equal to 75.
\n" ); document.write( "the only pattern i could find is this.
\n" ); document.write( "

\r\n" );
document.write( "-21\r\n" );
document.write( "-21 + 12 = -9\r\n" );
document.write( "-9  + 20 = 11\r\n" );
document.write( "11  + 28 = 39\r\n" );
document.write( "

\n" ); document.write( "if you look at the differences of 12, 20, and 28, you will see that the difference increases by 8 each time.
\n" ); document.write( "this means that the next number in the sequence would have to be 39 + 36, because 36 is equal to 28 + 8.
\n" ); document.write( "39 + 36 is equal to 75.
\n" ); document.write( "i derived the formula i used from this observation.\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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