SAT Math: Arithmetic


3, -6, 12, …

The first term in the sequence shown above is 3, and every term following is equal to -2 times the preceding term.  Out of the first 30 terms in this sequence, how many are less than 50?

A.  5
B.  6
C.  15
D.  18
E.  27

Knowsys Method

Read the problem carefully.  Make note of how the sequence works and note that you are focusing on the first 30 terms in the sequence only.  

Identify the bottom line.  Out of the first 30 terms, how many are less than 50?

Assess your options.  You could follow the sequence, list out the first 30 terms, and count how many terms are less than 50, but you do not need to do that much work.  Create a chart to help you notice the pattern, and use your logical thinking skills to help you figure out the answer.  

Attack the problem.  First, use your logical thinking skills.  Every other number in this sequence is going to be negative, and therefore less than 50.  So out of the first 30 terms, at least 15 of them will be less than 50. 

Next, create a chart of positions and values to help you figure out what positive values are also less than 50.  

Screen Shot 2013-12-23 at 10.21.01 AM.jpg

As you can see, 3 positive values in the sequence are less than 50.  Starting with the 7th term in the sequence, all positive values will be greater than 50.  So add 3 to 15, and you get 18 terms out of the first 30 that are less than 50.

Loop back.  Did we solve for the bottom line?  Yes.

The correct answer is D.

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