Sequence (Fibonacci numbers)

[ktn11]

1. A sequence 1, 1, 2, 3, 5, 8 ... from the second term, each term is the sum of the previous two terms. How many even numbers in the first 300 terms?

OA: 100

1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,1597,2584,4181,6765,......

As we can see here that in the first 10 terms we 3 even numbers (2,8,34). In the next 10 terms ie from 144.....6764 we again have 3 even numbers (144,610,2584) and hence i guess the pattern continues.

So in the first 100 terms we have 30 even numbers.Hence in first 300 terms we should have 90 even numbers

Is this correct? Any expert please explain

[Frankenstein]

Hi,
t1 is odd
t2 is odd
t3 is even
t4 = t3+t2 = even+odd = odd
t5 = t4+t3 = odd+even = odd
t6 = t5+t4 = odd+odd = even
t7 = t6+t5 = even+odd = odd
t8 = t7+t6 = odd+even = odd
t9 = t8+t7 = odd+odd = even
.
.
You can see the pattern, every third element is even and others are odd.
So, if there are 300 terms, every term is even means total number of even terms = 300/3 = 100.