Question

A badminton tournament begins with 512 teams. If a team loses once, it is eliminated from competition. After the first round, 256 teams remain. After the 4th round, how many teams remain? How many rounds will be required to determine the champion?

Answer 1

Answer:

This is GP with the first term of 512 and common ratio of 1/2

The formula for nth term is:

• aₙ = 512*(1/2)ⁿ

The number of teams after the 4th round:

• a₄ = 512*(1/2)⁴ = 32 teams

Number of rounds to determine the champion:

• 1 = 512*(1/2)ⁿ
• 2⁰ = 2⁹*2⁻ⁿ
• 0 = 9 - n
• n = 9 rounds

Answer 2

Answer:

The given sequence is in form of GP, where

a = 512 and common ratio (Tn/Tn-1) = 1/2.

We know that,

Tn = arn-1

• Tn = 512 × (1/2)^n
• T4 = 512 × 1/2^4
• T4 = 512 × 1/16
• T4 = 32

After 4 round, 32 teams will remain.

Now,

512 × (1/2)^n = 1

• 2^9 × 2^ -n = 2^0
• 9 - n = 0
• n = 9

So, 9th rounds will be required to determine the champion.