The fist two terms of a sequence are 1 and 2. Evey other term in the sequence is the sum of the two terms immediately preceding it. For example, the third term is 3 and the fourth terms is 2+3=5. How many of the fist 100 terms are odd?

How can i solve this easily?

Question

The fist two terms of a sequence are 1 and 2. Evey other term in the sequence is the sum of the two terms immediately preceding it. For example, the third term is 3 and the fourth terms is 2+3=5. How many of the fist 100 terms are odd?

How can i solve this easily?

anonymous · Answer

when you do the same you will get a sequence  1,2,3,5,8,13......
so you are getting a half add numbers        so    50 odd no. are present

angelab97 · Answer

thanks but my key says 67

anonymous · Answer

ya your right when we add more odd no. are comming  there should be some formula  
i dont know

angelab97 · Answer

okay thanks for the help

zzr0ck3r · Answer

well it will be every 3rd number starting at 3 will be even
so 66 of them + 1 and get 67

zzr0ck3r · Answer

start with 3
odd + even is odd (3+2) = 5
then
odd + odd is even

zzr0ck3r · Answer

so it will be odd odd even odd odd even starting at 3

angelab97 · Answer

okay thanks :)

angelab97 · Answer

but this is a PSAT question how can I make this problem solving easier?

zzr0ck3r · Answer

I don't know

angelab97 · Answer

okay, thanks anyways

zzr0ck3r · Answer

(2/3)(99)+1

angelab97 · Answer

what is the 2/3 for

zzr0ck3r · Answer

(2/3)
starting at 2 (2/3) of the rest of the numbers are odd

zzr0ck3r · Answer

the pattern starts with 2
e o o e o o e o o....
before that its 1 = 0, 2 = e
so that messes up the pattern if we start at 1
so we start at 2
so we have 99 terms left
and we know (2/3) of those terms are odd
(2/3)99, then we + 1 for the first term (1)

zzr0ck3r · Answer

you can prove the pattern as well