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 ?

Answer 1

The no. of variations in sign is 3

Explanation:

Variation in sign occurs when every single time a negative product is produced by a pair of consecutive terms.

Therefore, the determination of the number of changes in sign in the given sequence is must.

Therefore, we take the product of the pair of consecutive terms as:

`1* (-3)` = - 3, variation in sign

`(-3)* 2` = - 6, variation in sign

`2* 5` = 10, no sign variation

`5* (- 4)` = - 20, variation in sign

`- 4* (-6)` = 24, no sign variation