Rahul father wants to deposit some amount of money every year on the day of Rahul birthday. on his 1st birthday Rs.100,On his 2nd birthday Rs.300,On his 3rd birthday Rs. 600,On his 4th birthday Rs. 1000 and so on.what is the amount deposited by his father on Rahul 15th birthday
Answers
a=100
d = 200
a15 = 100 + 14*200
= 100 + 2800
= 2900
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Answer:
Step-by-step explanation:
Multiples of 2: 2;4;...........100
Multiples of 5: 5;10..........100
In the above series some numbers are repeated twice these are multiples of 10 i.e LCM of 2 and 5
Sum of integers which are divisible by 2 and 5 from 1 to 100=
(Sum of integers which are divisible by 2 from 1 to 100) + (sum of integers which are divisible by 5 from 1 to 100) -(sum of integers which are divisible by 10 from 1 to 100) =
(2+4+......... +100) +(5+10+...... +100) -(10+20+...... 100)
=2(1+2+3+....... 50) + 5(1+2+3+.......20) -10(1+2+3+..... +10) =
2(50(50+1)) ÷2 + 5(20(20+1)) ÷2 -10(10(10+1)) ÷2
=(50(51)) +5(10(20+1) -5(10(11) =
50(51) +5(10(21)-5(10(11) =
2550+1050-550=
3600-550
=3050
Therefore sum of integers from 1 to 100 which are divisible by 2 or 5 is 3050