document.write( "Question 838068: sequence 4,12,.....972\r
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Algebra.Com's Answer #505238 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
sequence 4,12,.....972\r
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If so then d = 12-4 = 8, a1 = 4\r\n" );
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document.write( "an = a1+(n-1)d\r\n" );
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document.write( "We see if 972 can be = an for some natural number n\r\n" );
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document.write( "972 = 4 + (n-1)(8)\r\n" );
document.write( "972 = 4 + 8n - 8\r\n" );
document.write( "972 = 8n - 4\r\n" );
document.write( "976 = 8n\r\n" );
document.write( "122 = n\r\n" );
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document.write( "Yes, since 122 is a natural number, and 972 is term number 122.\r\n" );
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document.write( "So\r\n" );
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document.write( "an = a1+(n-1)d  becomes\r\n" );
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document.write( "an = 4+(n-1)8 = 4+8n-8 = 8n-4\r\n" );
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\n" ); document.write( "sequence 4,12,.....972\r
\n" ); document.write( "\n" ); document.write( "can this be geometric, if so what is equation for nth term and what term number is 972?
If so then r = 12/4 = 3, a1 = 4\r\n" );
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document.write( "an = a1rn-1\r\n" );
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document.write( "We see if 972 can be = an for some natural number n\r\n" );
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document.write( "972 = 4·3n-1\r\n" );
document.write( "Divide both sides by 4\r\n" );
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document.write( "243 = 3n-1\r\n" );
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document.write( "We can break 243 as 35\r\n" );
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document.write( "35 = sn-1\r\n" );
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document.write( "So the exponents of 3 must be equal:\r\n" );
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document.write( "5 = n-1`\r\n" );
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document.write( "6 = n\r\n" );
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document.write( "Yes, since 6 is a natural number.  In fact since 6 isn't so large,\r\n" );
document.write( "we can write the sequence to 6 terms, though it isn't necessary,\r\n" );
document.write( "it's just a check:\r\n" );
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document.write( "4, 12, 36, 108, 324, 972\r\n" );
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document.write( "So 972 really is term number 6.\r\n" );
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document.write( "an = a1rn-1  becomes\r\n" );
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document.write( "an = 4·3n-1\r\n" );
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document.write( "Edwin
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