Tim Gan Math
All Years

1984 TYS

Question 1

Question

  1. The sum, ${{S}_{n}}$, of the first $n$ terms of an arithmetic progression is given by ${{S}_{n}}=pn+q{{n}^{2}}$.
    Given also that ${{S}_{3}}=6$ and ${{S}_{5}}=11$,
    1. Find the values of $p$ and $q$.

      [3]

    2. Deduce, or find otherwise, an expression for the $n$-th term and the value of the common difference.

      [3]

  2. Find the set of values of $\theta $ lying in the interval $-\frac{1}{2}\pi <\theta <\frac{1}{2}\pi $ such that the sum to infinity of the geometric series $1+\sin \theta +{{\sin }^{2}}\theta +\ldots $ is greater than $2$.

    [4]