Answer :

**Given:** Total teams in tournament are 16

Total prize money is Rs 8000

The last placed team is awarded Rs. 275

**To find:** Amount received by first place team

As the award money is increased by the same amount for successive finishing place, it forms an A.P.

Let a is amount receievd by first place team and d is successive increase in award

A.P. will be a, a + d, a + 2d,……………………

According to question:

n = 16, S_{16} = 8000 and a_{16} = 275

**Formula used:**

a_{n} = a + (n – 1)d

where a is first term, d is common difference and n is number of terms in an A.P.

Therefore,

a_{16} = a + (16 – 1)d

⇒ 275 = a + 15d

⇒ a = 275 – 15d …………(1)

⇒ 1000 = 2a + 15d …………(2)

Now put the value of a from (1) in (2):

⇒ 1000 = 2(275 – 15d) + 15d

⇒ 1000 = 550 – 30d + 15d

⇒ 1000 = 550 – 15d

⇒ 15d = 550 – 1000

⇒ 15d = –450

⇒ d = -30

Put d = -30 in (1):

a = 275 – 15(-30)

⇒ a = 275 + 450

⇒ a = 725

**Hence, amount received by first placed team is Rs. 725**

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