<PRE><B>Question 1209400</B>
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I doubt if there is a faster way to solve the problem than what is shown by the other tutor... but his response has a lot of unnecessary discussion at the beginning.&lt;br&gt;
The given recursive formula tells us how to get the next numbers in the sequence from the previous numbers in the sequence:&lt;br&gt;
a_n = a_(n-1) + a_(n-2)&lt;br&gt;
Turn that recursive formula around so it tells you how to find PREVIOUS numbers in the sequence from known numbers in the sequence:&lt;br&gt;
a_(n-2) = a_n - a_(n-1)&lt;br&gt;
Then, starting with the given a_11 = 4 and a_10 = 1...&lt;br&gt;
a_9 = a_11 - a_10 = 4-1 = 3&lt;br&gt;
a_8 = a_10 - a_9 = 1-3 = -2&lt;br&gt;
a_7 = a_9 - a_8 = 3-(-2) = 5&lt;br&gt;
a_6 = a_8 - a_7 = -2-5 = -7&lt;br&gt;
ANSWER: a_6 = -7
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