AbeNeedsAnswers wrote: ↑

Sun May 17, 2020 8:16 pm

Sam has $800 in his account. He will deposit $1 in his account one week from now, $2 two weeks from now, and each week thereafter he will deposit an amount that is $1 greater than the amount that he deposited one week before. If there are no other transactions, how much money will Sam have in his account 50 weeks from now?

A. $850
B. $1,200
C. $1,675
D. $2,075
E. $3,350

D

We have the following:

Initial amount of money: $800
Money after 1 week: $800 + $1
Money after 2 weeks: $800 + $1 + $2
Money after 3 weeks: $800 + $1 + $2 + $3
Money after 4 weeks: $800 + $1 + $2 + $3 + $4
.
.
.
Money after 50 weeks: $800 + $1 + $2 + $3 + $4 + . . . + $49 + $50
So we need to find the value of $1 + $2 + $3 + $4 + . . . + $49 + $50

Useful formula for the sum of the first n positive integers: 1 + 2 + 3 + ....+ n = n(n+1)/2

So 1 + 2 + 3 + ....+ 49 + 50 = 50(50+1)/2 = (50)(51)/2 = (25)(51) = 1275
So, $1 + $2 + $3 + $4 + . . . + $49 + $50 = $1275

So, the money after 50 weeks = $800 + $1275 = $2075

Answer: D

Cheers,
Brent