Question

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 the sequence 1, –3, 2, 5, –4, –6 ?

A. 1
B. 2
C. 3
D. 4
E. 5

Answer 1

Option C.

Explanation:

The given given sequence is

1, –3, 2, 5, –4, –6

We need to find the pairs of consecutive terms of the sequence and their product.

Pairs of consecutive terms | Product

1, -3 -3

-3, 2 -6

2, 5 10

5, -4 -20

-4, -6 24

Here the product of three pairs of consecutive terms is negative.

The number of variations in sign for the sequence is 3. Therefore, the correct option is C.