<u>Answer:</u>
<em><u>-7, -10</u></em>
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<u>Explanation:</u>
To solve this problem we must first understand what the pattern is in the sequence. Once we understand the pattern, we can then apply it to the final known term to find the next two terms.
Take a look at the sequence given:
<em>8, 5, 2, -1, -4,...</em>
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Let's start by figuring out how they got the second term in the sequence. To do that, identify what basic operation and number must be applied. This will reveal the pattern.
<em>8 - first term</em>
<em>5 - second term</em>
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<em>8 ? ? = 5</em>
<em>8 - 3 = 5</em>
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So, this means they subtracted three to get the next term. Therefore, the pattern should be 'subtract three' to get the next term. Just to be sure the pattern we found is correct, apply it to the given sequence.
<em>8, 5, 2, -1, -4,...</em>
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<em>8 </em><em>- 3 = </em><em>5</em>
<em>5 </em><em>- 3 = </em><em>2</em>
<em>2 </em><em>- 3 = </em><em>-1</em>
<em>-1 </em><em>- 3 = </em><em>-4</em>
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So, since 'subtracting three' every time gives us the next term, the pattern is correct.
Finally, let's continue the pattern to find the next two terms.
<em>-4 </em><em>- 3 = </em><em>-7</em>
<em>-7 </em><em>- 3 = </em><em>-10</em>
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Therefore, the next two terms in the sequence are <em><u>-7, -10.</u></em>
