# 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.

Money deposited by Rahul's father is as follows:

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

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