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) \(\frac{S_{15}}{a_{15}}>0\)
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
21. Given tha \(a\) and \(b\) are real numbers such that \(a>b>0\). Find the minimum value of
\(\sqrt 2 a^3 + \frac{3}{ab-b^2}\).
22. For how many integers \(n\), is \(n^2 + n + 1\) a divisor of \(n^{2019}+20\)?
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.
24. Four tennis balls are arranged as shown. Find the maximum height, in units, of the formation.
25. Find the minimum integral value of \(n\) in
\(x_1^3 + x_2^3 + x_3^3 + … + x_n^3 = 2002^{2002}\)
Baca juga:
SEAMO PAPER F 2021
SEAMO PAPER F 2020
SEAMO PAPER F 2019