Bunuel wrote:
Each term in sequence S is determined by multiplying the prior term by 2 and dividing that product by 3. What is the 100th term of the sequence S?
(1) The sum of the first 2 terms is 15
(2) The first term of the sequence is 9
Target question: What is the 100th term of the sequence S? Given: Each term in sequence S is determined by multiplying the prior term by 2 and dividing that product by 3. In other words, if term_n = k, then term_(n+1) = (2/3)k
IMPORTANT: once we know the value of ANY term in the sequence, we can determine every other term in the sequence.
Statement 1: The sum of the first 2 terms is 15 Let x = term1
So, (2/3)x = term2
We can write: x + (2/3)x = 15
Since we COULD solve this equation for x, we COULD determine the value of the first term in the sequence, which means we COULD calculate every term in the sequence.
So, we COULD find
the value of term100.
Since we COULD answer the
target question with certainty, statement 1 is SUFFICIENT
NOTE: Of course, we're not going to actually calculate the 100th term, since doing so would be a waste of precious time
Statement 2: The first term of the sequence is 9 Now that we know the value of the first term in the sequence, we COULD calculate every term in the sequence.
So, we COULD find
the value of term100.
Since we COULD answer the
target question with certainty, statement 2 is SUFFICIENT
Answer:
Cheers,
Brent
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