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In the first week of the year, Nancy saved $1. In each of the next 51 weeks, she saved $1 more than she had saved in the previous week. What was the total amount that Nancy saved during the 52 weeks?
A. $1,326
B. $1,352
C. $1,378
D. $2,652
E. $2,756
視頻解析
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文字解析
Arithmetic O
In dollars, the total amount saved is the sum of 1, (1 + 1), (1 + 1 + 1), and so on, up to and including the amount saved in the 52nd week, which was $52. Therefore, the total amount saved in dollars was 1 + 2 + 3 + … + 50 + 51 + 52. This sum can be easily evaluated by grouping the terms as (1 + 52) + (2 + 51) + (3 + 50) + … + (26 + 27), which results in the number 53 added to itself 26 times. Therefore, the sum is (26)(53) = 1,378.
Alternatively, the formula for the sum of the first n positive integers is 
. Therefore, the sum of the first 52 positive integers is 
.
The correct answer is C.
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