Answer:
7 rounds were played.
Step-by-step explanation:
A wrestling tournament begins with 128 competitors. In every round competitor has 1 match against another wrestler and winner moves to the next round. We have to construct a sequence representing all rounds of this tournament.
In first round total matches played = 128/2 = 64
In second round number of matches played = 64/2 = 32
In third round matches played = 32/2 = 16
Similarly all the rounds were played.
Now we get the sequence as 64, 32, 16, 8, 4, 2, 1
This sequence is a geometric sequence having first term 64
Common factor = 32/64 = 1/2
Number of terms = 7
Explicit rule ![a_{n}= a(r)^{n-1}=64.(\frac{1}{2})^{n-1}](https://tex.z-dn.net/?f=a_%7Bn%7D%3D%20a%28r%29%5E%7Bn-1%7D%3D64.%28%5Cfrac%7B1%7D%7B2%7D%29%5E%7Bn-1%7D)
Total seven rounds were played.