2 problems

[Guest]

Question 1. For a finite sequence of nonzero numbers, the number of variations in sign is defined as the number of pairs of consecutive terms of the sequence for which the product of the two consecutive terms is negative. What is the number of variations in sign for sequence 1,-3,2,5,-4,-6?


Question 2. n is a multiple of 5, n=p^2q where p and q are prime numbers. Which of the following must be a multiple of 25?
a) p^2
b) q^2
c) pq
d)p^2q^2
e)p^3q

Thank you!

 

[stapel]

1) Look at the numbers. Look at their signs. As you go from the first number in the sequence to the last, how many times does the sign change?

2) If n, the product of primes, is also a multiple of 5, then what must be true of at least one of the primes?

Eliz.

 

[Guest]

1) does it cange 3 times?

2) p^2?

 

[stapel]

1) does it cange 3 times?

If you mean "Does the sign change three times?", then the answer is "yes".

2) p^2?

Don't guess. Follow the reasoning.

Eliz.