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The sequence x1, x2, ..., xn is such that xn is such that x1 = 5, x2 =

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The sequence x1, x2, ..., xn is such that xn is such that x1 = 5, x2 = [#permalink] New post   20 Feb 2020, 05:18
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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


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D
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Re: The sequence x1, x2, ..., xn is such that xn is such that x1 = 5, x2 = [#permalink] New post   20 Feb 2020, 06:23
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Bunuel wrote:
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


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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
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Re: The sequence x1, x2, ..., xn is such that xn is such that x1 = 5, x2 = [#permalink] New post   20 Feb 2020, 07:10
Bunuel wrote:
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


\(x_n = x_{n-5}\) => 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
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Re: The sequence x1, x2, ..., xn is such that xn is such that x1 = 5, x2 = [#permalink] New post   17 Jun 2023, 00:54
Bunuel wrote:
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= ?


Given sequence is
5, -5, 0, -2, 4

After every 5 terms, sum is increased by 2.

\(S_p=S_p-3=18\)

Given answers:
\(S_{39}=2*7+(5-5+0-2)=12\)
\(S_{42}=2*8+(5-5)=16\)
\(S_{45}=2*9=18\)
\(S_{48}=2*9+(5-5+0)=18\)
\(S_{51}=2*10+(5)=25\)

45 corresponds to p-3, 48 corresponds to p.
Hence, \(=48\) (D)
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Re: The sequence x1, x2, ..., xn is such that xn is such that x1 = 5, x2 = [#permalink]
17 Jun 2023, 00:54
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