Hi guys, need help.
How can you tell when the two coincide for the first time using numbers?
The answer is at the 24th bar.
I used my CAS to calculate each sequence up to their 24th bar, and when looking at the two numbers from either sequence I didn't see any relevance.
Thanks in advance.
Okay, so the question is a rather confusing one - let's just differentiate what each part means and change the symbols up a bit:
We'll let
be the sequence we use for the crash cymbals, and
be the sequence we use for the timpani rolls. Now,
refers to the how much the instrument has already sounded - i.e., the
th sound. Now, the value that
and
take on are the bar in which the sound occurs.
So, what we want is to find the first point when
, and whatever value that is is our answer. Now, we note that
must be a multiple of three, since we start with 3 and keep doubling it, whereas
is an arithmetic sequence, and so could take any value. So, we will take
, and keep calculating values until we have a multiple of three, and that should be our answer. We will then double check this against
, since not every multiple of three will appear:
And so, we see that both sequences first take on the same value of 24, which is the bar that they first play together. The fact that they are at different positions only means that the cymbals have sounded more than the timpani at the time of this co-incision.