Question

In a football World Cup several teams participated. If the last place team in the point table receive $40,000 as a  prize money and the award increases by $2500 for the successive finishing places. The champion team receives $65,000. Find how many teams participated in the world cup?
1. 9
2. 12
3. 10
4. 11

Answer 1

Correct Answer - Option 4 : 11

Given∶

Last team received $ 40,000.

Champion team received $ 65,000.

Award increases by $2500 for the successive finishing places.

Formula Used∶

nth term of A.P. = a + (n - 1)d

Calculation∶

Prizes received by the teams in increasing order are, $ 40,000, $ 42500, $ 4500, $47500,.........

This is an A.P. with a = 40,000, d = 2500 and l = 65,000

Let the number of terms be n. Then,

a_n = 65000

a + (n - 1)d = 65000

⇒ 40000 + (n - 1) × 2500 = 65000

⇒ (n - 1) × 2500 = 65000 - 40000

⇒ (n - 1) = 25000/2500

⇒ n - 1 = 10 

⇒ n = 10 + 1 = 11

∴ 11 teams participated in Football World Cup.