Question

In the sequence -2, 4, 8..., each term after the second can be found by multiplying the two preceding terms together. For example, the third term is −2×4=−8. How many of the first 139 terms of this sequence are negative?

a) 45

b) 46

c) 47

d) 48

Answer 1

In the given sequence, negative terms appear every three terms. Counting up to the 139th term, there are 46 negative terms. Therefore, the answer is 46.

Step-by-step explanation:

To find out how many of the first 139 terms of the sequence are negative, we analyze the pattern of multiplication of terms. Given the sequence starts with -2, 4, and each term is produced by multiplying the two preceding terms, we can use the multiplication rules for signs to determine the sign of each subsequent term:

• When two positive numbers multiply, the result is positive.
• When two negative numbers multiply, the result is positive.
• When two numbers with opposite signs multiply, the result is negative.

Observing this sequence, we can see that every term after the initial negative term will be as follows:

1. The first term is negative (-2).
2. The second term is positive (4).
3. The third term will be negative since we're multiplying a negative by a positive (-2 x 4 = -8).
4. The fourth term will again be positive since we're multiplying two negative terms together (-2 x -8 = 16).
5. The fifth term will be negative since we're multiplying a positive by a negative (4 x -8 = -32).
6. This pattern will repeat with two successive positive terms followed by one negative term.

Thus, every third term starting from the third term is negative. To find the number of negative terms among the first 139 terms, divide 139 by 3. This yields 46 with a remainder. Since the 139th term will not complete the next pattern of three, it must be positive, meaning we do not count it as negative.

Therefore, the answer is 46.