29. A children society decided to give ten cash prizes to the students of a school for their overall academic performance.
They decided to distribute 3750 among 10 students. If each prize is 50 less than the preceding prize, find the
value of each prize.
Answers
Answer:
1=600
2=550
3=500
4=450
5=400
6=350
7=300
8=250
9=200
10=150
Step-by-step explanation:
x+x+50+x+100+x+150+x+200+x+250+x+300+x+350+x+400+x+450=3750
10x+2250=3750
10x=1500
x=150
0n value sustitution
1=600
2=550
3=500
4=450
5=400
6=350
7=300
8=250
9=200
10=150
Answer:
Let the value of the prices be
x,x−50,x-100, .....
This is an arithmetic sequence with first term (a)=xand common difference (d)=−50.
Given,
Sn = 3750
d=-50
n=10
Using the formula:
Sn= n/2[2a + (n - 1)d]
3750=5(2a+9×-50)
750+450=2a
a=600
hence the first term of the AP is 600
first student will get rupees 600
2nd student will get rupees 550
third student will get rupees 500
fourth student will get rupees 450
fifth student will get rupees 400
sixth student will get rupees 350
seventh student will get rupees 300
8th student will get rupees 250
ninth student will get rupees 200
10th student will get rupees 150