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Опрос |
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GMAT/Problem Solving - Sequence Sixty
Sequence Sixty
What is the sixtieth term in the following sequence?
1, 2, 4, 7, 11, 16, 22...
(A) 1,671
(B) 1,760
(C) 1,761
(D) 1,771
(E) 1,821
| ОТВЕТЫ И КОММЕНТАРИИ |
| Решение |
Noting that a1 = 1, each subsequent term can be calculated as follows:
a1 = 1
a2 = a1 + 1
a3 = a1 + 1 + 2
a4 = a1 + 1 + 2 + 3
ai = a1 + 1 + 2 + 3 + ... + i-1
In other words, ai = a1 plus the sum of the first i - 1 positive integers. In order to determine the sum of the first i - 1 positive integers, find the sum of the first and last terms, which would be 1 and i - 1 respectively, plus the sum of the second and penultimate terms, and so on, while working towards the median of the set. Note that the sum of each pair is always equal to i:
1 + (i - 1) = i
2 + (i – 2) = i
3 + (i – 3) = i
…
Because there are (i - 1)/2 such pairs in a set of i - 1 consecutive integers, this operation can be summarized by the formula i(i - 1)/2. For this problem, substituting a1 = 1 and using this formula for the sum of the first (i-1) integers yields:
ai = 1 + (i)(i - 1)/2
The sixtieth term can be calculated as:
a60 = 1 + (59)(60)/2
a60 = 1,771
The correct answer is D.
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Politicians are primarily concerned with their own survival; artists are
concerned with revealing truth. Of course, the difference in their reactions is
readily predictable. For example, while the governmental leaders wrote laws to
ensure the triumph of industrialization in Western Europe, artists painted,
wrote about, and composed music
in response to the horrible conditions created by the Industrial Revolution.
Only later did political leaders come to see what the artists had immediately
perceived, and then only through a glass darkly. Experience teaches us
that___________.
Which of the following represents the most logical continuation of the passage?
A) artistic vision perceives in advance of political practice
B) artists are Utopian by nature while governmental leaders are practical
C) throughout history political leaders have not been very responsive to the
needs of their people
D) the world would be a much better place to live if only artists would become
kings
E) history is the best judge of the progress of civilization
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Вверх 
