# Q : 16         A sum of Rs $\small 700$ is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is Rs $\small 20$ less than its preceding prize, find the value of each of the prizes.

It is given that
Each price is decreased by 20 rupees,
Therefore,  d = -20 and there are total 7 prizes so n = 7 and sum of prize money is Rs 700 so $S_7 = 700$
Let a be the prize money given to the 1st student
Then,
$S_7 = \frac{7}{2}\left \{ 2a+(7-1)(-20) \right \}$
$700 = \frac{7}{2}\left \{ 2a-120 \right \}$
$2a - 120 = 200$
$a = \frac{320}{2}= 160$
Therefore, the prize given to the first student is Rs 160
Now,
Let $a_2,a_2,...,a_7$ is the prize money given to the next 6 students
then,
$a_2 = a+d = 160+(-20)=160-20=140$
$a_3 = a+2d = 160+2(-20)=160-40=120$
$a_4 = a+3d = 160+3(-20)=160-60=100$
$a_5 = a+4d = 160+4(-20)=160-80=80$
$a_6 = a+5d = 160+5(-20)=160-100=60$
$a_7 = a+6d = 160+6(-20)=160-120=40$
Therefore, prize money given to 1 to 7 student is 160,140,120,100,80,60.40

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