<p>Okay so I have a problem I don't understand from the Rocket Review book, and the explanation doesn't help. Could you please explain this to me? </p>
<p>The first two numbers of a sequence are 1 and 1. Every number after the second is the sum of the two numbers immediately preceding it, so the third number is 2, the fourth number is 3, the fifth number is 5, and so on. How many of the first 200 numbers in this sequence are odd?
The answer is 134, but I chose 133. </p>
<p>Care to explain? Thankyaa!</p>
<p>The pattern goes O O E O O E …Divide 200 by 3 and you get 66 remainder 2. So the pattern completes 66 times with 2 left over. That gives you 66 x 2 = 132 odd #s, and then both of the two leftovers are also odd (b/c the pattern begins with 2 odd #s…)</p>
<p>That’s what the book said…
I understand dividing 200 by 3, but I would just think to multiply (200/3) by 2, which would be 133.33333. Why would you not multiply the 2/3 that goes along with the 66 by 2 as well?</p>
<p>Try it with smaller numbers and see if it helps: suppose there were 6 numbers in the pattern. Since 6 divides evenly by 3, you get exactly 6/3=2 “sets” of OOE and so it is 2*2=4 odds. This IS (2/3) times 6 but as you will soon see, that doesn’t always work. </p>
<p>Now try 7 numbers. It is still 2 complete sets and also 1 more nummber which happens to be odd (because the pattern begins with 2 odds followed by the even). So the answer is 4 + 1 =5. But if you try (2/3)x7 you get 4.333…</p>
<p>Now try 8 numbers. And it is still 2 complete sets, plus 2 this time because 8 is two more than the 6 that complete the pattern evenly.</p>