Problema Solution
Cherry made deposits from her school allowance as follows 10 pesos on the first week , 13 pesos on the second week 16 pesos on the third week and so on . How much was her total school allowance after 52 deposits ?
Answer provided by our tutors
First deposit:
a1 = 10
Second deposit:
a2 = a1 + 3
a2 = 10 + 3
Third deposit:
a3 = a2 + 3
a3 = a1 + 3 + 3
a3 = a1 + 2*3
n-th deposit:
an = a1 + (n-1)*3
For n = 52 we have:
a52 = a1 + (52 - 1)*3
a52 = 10 + 51*3
a52 = $163
The total school allowance deposit after 52 deposits is:
a1 + a2 + ... +a52 = 10 + 10 + 1*3 + ....+10 + 51*3 = 52*10 + 3(1 + 2 + 3 + ... + 51) = 520 + 3*(1/2)51*(51 + 1) = $4498