SAT Math Multiple Choice Practice Question 395: Answer and Explanation

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Question: 395

21. 2,-4,-8,…

In the sequence above, each term after the second is equal to the product of the two preceding terms. For example, the third term, -8, is the product of 2 and -4. How many of the first 100 terms of this sequence are negative?

A. 33
B. 34
C. 50
D. 66
E. 67

Correct Answer: D


D In this problem, only the signs of the terms matter. By following the rule of the sequence, you should see that the first six terms of the sequence are +, –, –, +, –, –,…. The pattern {+, –, –} repeats forever. In the first 100 terms, the pattern repeats times. Because each repetition contains two negative numbers, in 33 full repetitions there are negative numbers. The 100th term is the first term of the next pattern, which is positive, so the total number of negative terms is 66.

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