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28 Apr 2020, 07:08
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Difficulty:
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Question Stats:
85% (01:46) correct
15%
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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
PS44321.02
A. $850
B. $1,200
C. $1,675
D. $2,075
E. $3,350
PS44321.02
28 Apr 2020, 09:16
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parkhydel
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
PS44321.02
A. $850
B. $1,200
C. $1,675
D. $2,075
E. $3,350
PS44321.02
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: \(1 + 2 + 3 + ....+ n = \frac{n(n+1)}{2}\)
So \(1 + 2 + 3 + ....+ 49 + 50 = \frac{50(50+1)}{2}= \frac{(50)(51)}{2}= (25)(51) = 1275\)
So, $1 + $2 + $3 + $4 + . . . + $49 + $50 = $1275
So, the money after 50 weeks = $800 + $1275 = $2075
Answer: D
Cheers,
Brent
13 Dec 2020, 06:04
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parkhydel
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
PS44321.02
Solution:A. $850
B. $1,200
C. $1,675
D. $2,075
E. $3,350
PS44321.02
The total amount of money Sam will have 50 weeks from now is:
800 + (1 + 2 + 3 + … + 50)
The sum (1 + 2 + 3 + … + 50) can be easily calculated by using the formula sum = average x number. The average of this equally-spaced set is (first + last)/2 = (1 + 50)/2, and we note that there are 50 terms (numbers) comprising the sum.
= 800 + (1 + 50)/2 x 50
= 800 + 51 x 25
= 800 + 1275
= $2075
Answer: D
