Question

a sequence of numbers begin with the numbers -10, 20, 30,..., and each term afterward is the product of the preceding three terms. how many of the first 101 terms of this sequence are positive?

Answer 1

If you think of the problem being just a series of multiplied signs it looks something like this...\[- * + * + * - * - * + * + * ...\]As you can see, after the first term it follows a pattern of..

[2 Positive] -> [2 Negative] -> [2 Positive] -> etc.

This means that for that set of terms half will be positive and half will be negative, which is convenient since the set represents 100 out of the 101 terms leaving one extra negative at the beginning of the pattern.

So, out of the first 101 terms, 50 are positive and 51 are negative.