Rahul’s father wants to deposit some amount of money every year on the day of Rahul’s birthday. On his 1st birth day Rs.100, on his 2nd birth day Rs.300, on his 3rd birth day Rs.600, on his 4th birthday Rs.1000 and so on. What is the amount deposited by his father on Rahul’s 15th birthday.
Answers
Answer:
12000
Step-by-step explanation:
Money deposited by Rahul's father is as follow
100, 300, 600, 1000
They are in following series
100 + 1*0, 100 + 2 * 100, 300 + 3 * 100, 600 + 4*100
Multiplication numbers 1, 2, 3 & 4 represent the age Rahul is turning.
The multiplication factor is previous year deposit.
If we say, n is number of years, Rahul is turning and T1 = 100. Then the series can be re written as (T0 = 0)
T1 + n*T0,
T2 = T1 + n*100,
T3 = T2 + n*100 = T1 + (n-1)*100 + n*100
T4 = T3 + n*100 = T1 + (n - 2)*100 + (n - 1)*100 + n*100
....
T15 = T14 + 15*100
= 1*100 + 2*100 + 3*100 + ........+ 15*100
All the terms after T1 are in AP where, nth term is sum of n terms of the AP where
a = 100 and d = 100 n = 15
Hence T15 =
= n(2a + (n-1)d)/2
= 15(200 + 14*100)/2
= 15 *800
= 12000
Answer:
Rs 12000
Step-by-step explanation:
Rahul’s father wants to deposit some amount of money every year on the day of Rahul’s birthday. On his 1st birth day Rs.100, on his 2nd birth day Rs.300, on his 3rd birth day Rs.600, on his 4th birthday Rs.1000 and so on. What is the amount deposited by his father on Rahul’s 15th birthday.
Deposited on 1st Birthday = Rs 100 = ( 0 + 1 * 100)
Deposited on 2nd Birthday = Rs 300 = ( 100 + 2 * 100)
Deposited on 3rd Birthday = Rs 600 = ( 300 + 3 * 100)
Deposited on 4th Birthday = Rs 1000 = (600 + 4 * 100)
Every month he deposits = Last month deposit + Month number * 100
15 Month = 14 Month + 15 * 100
14 month = 13 month + 14 * 100
13 Month = 12 Month * 13 * 100
3rd Month = 2nd Month + 3*100
2nd Month = 1st Month + 2 * 100
1st Month = 0 + 1 * 100
Deposit on 15th Month = (15 * 100) + (14 * 100) + (13* 100) + ......+ (3*100)+ (2*100) +(1*100)
= 100 * ( 15 + 14 + 13 + .............. + 3 + 2 + 1)
= 100 * 15 * 16/2
= 12000
Rs 12000 he deposited on 15th Birthday