Question

In a cricket tournament 16 school terms participated. A sum of $Rs.8000$ is to be awarded among themselves as prize money. If the last placed term is awarded $Rs275$ in prize money and the award increases by the same amount for successive finishing places, how much amount will the first place team receive ?

Answer 1

$T_n=a+(n-1)d$

$275=a+(16-1)d$

$275=a+15d$...(1)

$S_n=\frac{n}{2}[2a+(n-1\left)d\right]$

$S_{16}=\frac{16}{2}[2a+(16-1\left)d\right]$

$8000=8[2a+15d]$

$1000=2a+15d$...(2)

(2)-(1) gives:

$(2a+15d)-(a+15d)=1000-275$

$a=725$

Therefore Rs.725 is received by the first place team.