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rohan2345
Except for the first two numbers, every number in the sequence –1, 3, 2, . . . is the sum of the two immediately preceding numbers. How many numbers of this sequence are even?

(A) none
(B) one
(C) two
(D) three
(E) more than three

Let's expand the series - { -1 , 3 ,2, 5 , 7 , 12, 19 , 31 , 50 , 81 , 131 , 212.............. }

Thus, by adding a few numbers ( Actually ) we come to know that the correct answer will be (E) more than three
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rohan2345
Except for the first two numbers, every number in the sequence –1, 3, 2, . . . is the sum of the two immediately preceding numbers. How many numbers of this sequence are even?

(A) none
(B) one
(C) two
(D) three
(E) more than three

We are given the sequence –1, 3, 2, ... Let’s denote this sequence by a(n). So we have a(1) = –1, a(2) = 3, and a(3) = 2. Let’s also find a few more terms of the sequence. Keep in mind that every term after the first two terms is the sum of the two immediately preceding terms.

a(4) = 3 + 2 = 5

a(5) = 2 + 5 = 7

a(6) = 5 + 7 = 12

a(7) = 7 + 12 = 19

a(8) = 12 + 19 = 31

a(9) = 19 + 31 = 50

As we can see, if n is a multiple of 3, then a(n) is even [notice that a(3) = 2, a(6) = 12, a(9) = 50]. Thus, terms such as a(12), a(15), ... will be also even. We can see that the number of terms that will be even must be more than three.

Answer: E
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