Question 1035524
From -1 to 2, we're multiplying by -2

From 2 to -4, we're multiplying by -2

From -4 to 8, we're multiplying by -2

and so on


The rule is this:
to get the next term, we multiply the previous term by -2


So the term after 8 is -16 because
8 times -2 = -16

and the term after -16 is 32 because
-16 times -2 = 32

etc etc


Let's generate up to the 10th term

<table border=1 cellpadding=3><tr><th>Term Number</th><th>Term</th><th>Notes</th></tr><tr><td>1</td><td>-1</td><td>Given</td></tr><tr><td>2</td><td>2</td><td>Given</td></tr><tr><td>3</td><td>-4</td><td>Given</td></tr><tr><td>4</td><td>8</td><td>Given</td></tr><tr><td>5</td><td>-16</td><td>8*(-2) = -16</td></tr><tr><td>6</td><td>32</td><td>-16*(-2) = 32</td></tr><tr><td>7</td><td>-64</td><td>32*(-2) = -64</td></tr><tr><td>8</td><td>128</td><td>-64*(-2) = 128</td></tr><tr><td>9</td><td>-256</td><td>128*(-2) = -256</td></tr><tr><td>10</td><td><font color=red>512</font></td><td>-256*(-2) = <font color=red>512</font></td></tr></table>


So the tenth term is <font color=red>512</font>


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Shortcut Method


First term is a = -1
Common ratio is r = -2


The nth term of this geometric sequence is {{{a*r^(n-1) = -1*(-2)^(n-1)}}}


Plug in n = 10 to get


{{{-1*(-2)^(n-1)=-1*(-2)^(10-1) = -1*(-2)^9 = -1*(-512) = 512}}}


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Either way, the final answer is <font color=red>512</font>