Question

A sum of Rs. 700 is to be used to give 7 cash prizes to students of a school for community service, in accordance with their contribution towards it. If each prize is Rs. 20
less than its preceding prize, then:

i)Calculate the value of each of the prizes.

ii)What do you think must be the qualities of these students who qualified for these prizes? (Mention any two)

Answer 1

l) we can let that a is the 1st term
n d be the common difference i.e 20
s is 700
n is 7
∴s=n/2 (2a+(n-1)d)
⇒s=n/2 (2a+(n-1)d)
⇒700 =7/2(2a+( 6)-20)
⇒1400=7(2A -120)
⇒1400=14a-840)
⇒1400+840=14a
∴a=2240/14
     =160
∴a₂ will be 160-20
               =140
1st price= rs160
2nd price=rs140
3rd price=rs120
4th price=rs100
5th price=rs80
n last 6th price=rs 40
ll) he has a giving nature 

Answer 2

i) from this question the A.P. form will be
a,a-20, a-40, a-60, a-80, a-100, a-120
sum of these A.P. will be
n/2{2a+(n-1)d}
=7/2{2a+(7-1)(20)}
it is given that sum of all the price is 700
so,
7/2{2a+(7-1)(-20)} = 700
or, 2a-120 = 200
or,. a= (200+120)/2
a=160
there for, the price are 160,140,120,100,80,60,40


ii) These student are very talented.

Don't forget to comment than you