Problem And Solution SEAMO 2017 Paper F

SEAMO

19. Let \(S_n\) be the sum of the first \(n\) terms of an arithmetic series \({a_n}\). If \(S_{15} > 0\) and \(S_{16} < 0\), which of the following is true?

(A) \(\frac{S_2}{a_2}<0\)
(B) \(\frac{S_8}{a_8}<0\)
(C) \(\frac{S_9}{a_9}<0\)
(D) \(\frac{S_{10}}{a_{10}}>0\)
(E) \(\frac{S_{15}}{a_{15}}>0\)


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20. Let \(b_k\) denote the coefficient of \(x^k\) for \((x+1)^3(x+2)^3(x+3)^3\).

Find \(b_2 + b_4 + b_6 + b_8\)

(A) 216
(B) 6696
(C) 6912
(D) 13824
(E) 3843


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21. Given tha \(a\) and \(b\) are real numbers such that \(a>b>0\). Find the minimum value of

\(\sqrt 2 a^3 + \frac{3}{ab-b^2}\).


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22. For how many integers \(n\), is \(n^2 + n + 1\) a divisor of \(n^{2019}+20\)?


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23. The sequences \({a_n}\) is defined by \(a_0=1, a_1=3\) and \(a_n=a_{n-1} + \frac{a_n^2}{a_{n-2}}\) for \(n≥2\).

The sequences \({b_n}\) is defined by \(b_0=1, b_1=1\) and \(b_n=b_{n-1} + \frac{b_n^2}{b_{n-2}}\) for \(n≥2\).

Find the value of \(\frac{a_{2017}}{b_{2017}}\), giving your answer in index form rounded ti the nearest whole number.


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24. Four tennis balls are arranged as shown. Find the maximum height, in units, of the formation.


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25. Find the minimum integral value of \(n\) in

\(x_1^3 + x_2^3 + x_3^3 + … + x_n^3 = 2002^{2002}\)


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Baca juga:
SEAMO PAPER F 2021
SEAMO PAPER F 2020
SEAMO PAPER F 2019

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