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04 Apr 2022, 02:13
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
83% (01:54) correct
17%
(02:52)
wrong
based on 191
sessions
History
Date
Time
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Not Attempted Yet
The infinite sequence \(a1, \ a2, \ …, \ an, \ …\) is such that \(a_1 = 3, \ a_2 = -1, \ a_3 = 6, a_4 = -2\), and \(a_n = a_{n-4}\) for \(n > 4\). What is the sum of the first 83 terms of the sequence?
A. 120
B. 124
C. 128
D. 132
E. 136
A. 120
B. 124
C. 128
D. 132
E. 136
09 Apr 2022, 11:00
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Given: The infinite sequence \(a1, \ a2, \ …, \ an, \ …\) is such that \(a_1 = 3, \ a_2 = -1, \ a_3 = 6, a_4 = -2\), and \(a_n = a_{n-4}\) for \(n > 4\).
Asked: What is the sum of the first 83 terms of the sequence?
a_1 + a_2 + a_3 + a_ 4 = 3 - 1 + 6 - 2 = 6
a_5 + a_6 + a_7 + a_8 = a_1 + a_2 + a_3 + a_ 4 = 6
...
Sum of each successive 4 terms = 6
83 = 20*4 + 3
Sum of first 83 terms = sum of first 80 terms = 20*6 + 3 - 1 + 6 = 120 + 8 = 128
IMO C
Asked: What is the sum of the first 83 terms of the sequence?
a_1 + a_2 + a_3 + a_ 4 = 3 - 1 + 6 - 2 = 6
a_5 + a_6 + a_7 + a_8 = a_1 + a_2 + a_3 + a_ 4 = 6
...
Sum of each successive 4 terms = 6
83 = 20*4 + 3
Sum of first 83 terms = sum of first 80 terms = 20*6 + 3 - 1 + 6 = 120 + 8 = 128
IMO C
27 Nov 2025, 18:13
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I cant understand this question, can anyone give a detailed explanation
