alanforde800Maximus wrote:Ques)A certain sequence consist of alternating positive and negative numbers.if the sequence begins with a negative number and contains K numbers, where K is odd, how many positive numbers are in the set?
a)(k+1)/2
b)(k-1)/2
c)k/(2+1)
d)k/(2-1)
e)k/2
Let's look for a pattern...
k = 1
NEGATIVE
0 positive numbers
k = 3
NEGATIVE, POSITIVE, NEGATIVE
1 positive number
k = 5
NEG, POS, NEG, POS, NEG
2 positive numbers
Notice that if we examine the first 4 numbers, HALF are positive (and the last number is negative).
k = 7
NEG, POS, NEG, POS, NEG, POS, NEG
3 positive numbers
Notice that if we examine the first 6 numbers, HALF are positive (and the last number is negative).
k = 9
NEG, POS, NEG, POS, NEG, POS, NEG, POS, NEG
4 positive numbers
Notice that if we examine the first 8 numbers, HALF are positive (and the last number is negative).
In general, if we examine the first k-1 numbers, HALF will be positive (and the last number is negative).
So, the number of positive numbers = half of (k-1)
= [spoiler](k-1)/2[/spoiler]
=
B
