Challenging Questions Mathematics – Compulsory Part Learning Unit: Arithmetic and geometric sequences and their summations Question M0-07-07 Consider a geometric sequence \(T_n=ar^{n-1}\) and the series of \(n\) terms \(S_n=\frac{a(r^n-1)}{r-1}\) where \(r \neq 1\), # More challenging questions will be updated # Answer
Challenging Questions Mathematics – Compulsory Part Learning Unit: Arithmetic and geometric sequences and their summations Question M0-07-06 # More challenging questions will be updated # Answer
Challenging Questions Mathematics – Compulsory Part Learning Unit: Arithmetic and geometric sequences and their summations Question M0-07-05 Find the minimum number of terms of a geometric sequence \(1, \frac{3}{2}, \frac{9}{4} \,……\,\) such that the sum is greater than \(1000\). # More challenging questions will be updated # Answer
Challenging Questions Mathematics – Compulsory Part Learning Unit: Arithmetic and geometric sequences and their summations Question M0-07-04 The first, third, and 13th terms of an arithmetic sequence form a geometric sequence. Find the common ratio of the geometric sequence. # More challenging questions will be updated # Answer
Challenging Questions Mathematics – Compulsory Part Learning Unit: Arithmetic and geometric sequences and their summations Question M0-07-03 In an arithmetic sequence, the sum of the first \(n\) terms is equal to the sum of the next \(n+1\) terms, where \(n \geq 1\). Which term in this sequence is equal to \(0\)? # More challenging questions... » read more
Challenging Questions Mathematics – Compulsory Part Learning Unit: Arithmetic and geometric sequences and their summations Question M0-07-02 If \(a^2\), \(b^2\) and \(c^2\) form an arithmetic sequence where \(a\), \(b\) and \(c\) are real numbers, show that \(\frac{1}{b+c}\), \(\frac{1}{c+a}\) and \(\frac{1}{a+b}\) also form an arithmetic sequence. # More challenging questions will be updated # Answer
Challenging Questions Mathematics – Compulsory Part Learning Unit: Arithmetic and geometric sequences and their summations Question M0-07-01 Consider a sequence \(a, b, c, \ldots \ldots\) # More challenging questions will be updated # Answer
Challenging Questions Mathematics – Compulsory Part Learning Unit: More about polynomials Question M0-04-10 \( (x – a) \) is a common factor of \( f(x) \) and \( g(x) \). # More challenging questions will be updated # Answer
Challenging Questions Mathematics – Compulsory Part Learning Unit: More about polynomials Question M0-04-09 Given the expression \( x^6 – a^6 \): # More challenging questions will be updated # Answer
Challenging Questions Mathematics – Compulsory Part Learning Unit: More about polynomials Question M0-04-08 Consider \( f(x) = a_n x^n + a_{n-1} x^{n-1} + \dots + a_2 x^2 + a_1 x + a_0 \). # More challenging questions will be updated # Answer
Challenging Questions Mathematics – Compulsory Part Learning Unit: More about polynomials Question M0-04-07 Given \( f(x) = (x + 1)g(x) \), show that \( f(x – 3) \) is divisible by \( (x – 2) \). # More challenging questions will be updated # Answer
Challenging Questions Mathematics – Compulsory Part Learning Unit: More about polynomials Question M0-04-06 Consider \( f(x) = 6x^4 – 19ax^3 + 13a^2x^2 + 4a^3x – 4a^4 \). # More challenging questions will be updated # Answer