document.write( "Question 1035524: Given the sequence -1,2,-4,8... What is the 10th term ? Write the number only \n" ); document.write( "

Algebra.Com's Answer #650183 by jim_thompson5910(35256) $\"\"$ $\"About$

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From -1 to 2, we're multiplying by -2\r
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\n" ); document.write( "\n" ); document.write( "From -4 to 8, we're multiplying by -2\r
\n" ); document.write( "\n" ); document.write( "and so on\r
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\n" ); document.write( "\n" ); document.write( "The rule is this:
\n" ); document.write( "to get the next term, we multiply the previous term by -2\r
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\n" ); document.write( "\n" ); document.write( "So the term after 8 is -16 because
\n" ); document.write( "8 times -2 = -16\r
\n" ); document.write( "\n" ); document.write( "and the term after -16 is 32 because
\n" ); document.write( "-16 times -2 = 32\r
\n" ); document.write( "\n" ); document.write( "etc etc\r
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\n" ); document.write( "\n" ); document.write( "Let's generate up to the 10th term\r
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Term Number	Term	Notes
1	-1	Given
2	2	Given
3	-4	Given
4	8	Given
5	-16	8*(-2) = -16
6	32	-16*(-2) = 32
7	-64	32*(-2) = -64
8	128	-64*(-2) = 128
9	-256	128*(-2) = -256
10	512	-256*(-2) = 512

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\n" ); document.write( "\n" ); document.write( "So the tenth term is 512\r
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\n" ); document.write( "\n" ); document.write( "Shortcut Method\r
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\n" ); document.write( "\n" ); document.write( "First term is a = -1
\n" ); document.write( "Common ratio is r = -2\r
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\n" ); document.write( "\n" ); document.write( "The nth term of this geometric sequence is $\"a%2Ar%5E%28n-1%29+=+-1%2A%28-2%29%5E%28n-1%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "Plug in n = 10 to get\r
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\n" ); document.write( "\n" ); document.write( "Either way, the final answer is 512 \n" ); document.write( "

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