Question 1122508
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The terms are all powers of 2.  So one way to make the problem easy is to use the fact that the sum of the powers of 3 from 0 to (n-1) is (2^n)-1.<br>
So let's start by adding the three terms 1, 2, and 4 to the beginning of the given sequence.  The sum is now 8184+7 = 8191.<br>
2^13 = 8192; that means our sequence with the three extra terms contains 13 terms -- from 2^0 to 2^12.<br>
Since we added 3 terms to the given sequence, the given sequence has 10 terms.<br>
Answer: 10 terms<br>
And, having written that response, here is something that might make the work even easier.<br>
We can divide every term in the given sequence by 8; then the question will be finding the number of terms in the sequence 1, 2, 4 ,8, ... that have a sum of 8184/8 = 1023.<br>
Since 2^10 = 1024, the immediate answer is 10 terms.