Every term of the series starting from the 3rd term is the sum of the two preceding terms. If the 1st term is odd, 2nd term is even and the total no of terms in the series is 150, then find the ratio of the no of even terms to the no of odd terms?? ans= 1:2.. approach plz

Suppose the first term of the series is 1 and the second term is 2. Thus as per given conditions the series will be 1,2,3,5,8,13,21,34,55,89,144,233,377... and so on. Here you will notice that the even terms in this series are at positions 2,5,8,11... and so on, which is an AP with common difference 3 and last term 149 (because we know that total terms in the series are 150, and the series has pattern of 3n-1). So now we can calculate the number of terms in the AP 2,5,8,11...149. which will be {(149-2)/3}+1=50.
So total number of even terms = 50.
total number of odd terms = 150-50=100.
Required Ratio = 50/100 = 1:2

1.odd+odd=even
2.odd+even=odd

odd, even, odd(2), odd(2), even(1), odd(2)... It forms a pattern. Odd even odd, odd even odd,...so on..
hence 1:2