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20 Feb 2020, 05:18
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D
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Difficulty:
75%
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Question Stats:
63% (02:29) correct
37%
(02:48)
wrong
based on 368
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The sequence \(x_1\), \(x_2\), ..., \(x_n\) is such that \(x_1 = 5\), \(x_2 = -5\), \(x_3 = 0\), \(x_4 = -2\), \(x_5 = 4\) and \(x_n=x_{n-5}\). If the sum of the first P terms as well as the sum of the first P-3 terms is 18, P= ?
A. 39
B. 42
C. 45
D. 48
E. 51
Are You Up For the Challenge: 700 Level Questions
A. 39
B. 42
C. 45
D. 48
E. 51
Are You Up For the Challenge: 700 Level Questions
20 Feb 2020, 06:23
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Bunuel
First step in any question of sequence is to find several terms and see the pattern
\(x_1 = 5\)
\(x_2 = -5\),
\(x_3 = 0\),
\(x_4 = -2\),
\(x_5 = 4\)
Because \(x_n=x_{n-5}\)
\(x_6 = x_1 = 5\)
\(x_7 = x_2 = -5\),
\(x_8 = x_3 = 0\),
\(x_9 = x_4 = -2\),
\(x_{1-} = x_5 = 4\)
Sum of first 5 terms = 2
18 = 2*9
i.e. there are 9 cycles needed
i.e. Total terms needed fro sum 18 = 9*5 = 45 terms
But sum of next three terms is Zero i.e .Sum of 48 terms = 18
hence, p = 48 and p-3 = 45
Answer: Option D
shameekv1989
20 Feb 2020, 07:10
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Bunuel
\(x_n = x_{n-5}\) => the fitst 5 terms repeat themselves in the set of 5
The sum of the first 5 terms is 2
Therefore for it to be 18 we need minimum 9 such sets
Therefore 9*5 = 45 but since the first 3 terms add to 0 as well P+3 i.e. the sum of 48 terms will also be 0
Therefore P = 48 and P-3 = 45 both will have a sum of 18
Answer - D
