In a geometric progression, the first term is 12 and the fourth term is $-\frac{3}{2}$. The sum of

Question

In a geometric progression, the first term is 12 and the fourth term is $-\frac{3}{2}$. The sum of the first $n$ terms of the progression is given by $S_n$ and the sum to infinity of the progression is given by $S$. Find the least value of $n$ for which $\left| S - S_n \right| < 0.001$.[5] An arithmetic progression has the first term 1000 and common difference $-1.5$. Calculate the value of the first negative term of the progression and the sum of all the positive terms.[4] The sum of the first $n$ terms of a series is given by $S_n = \frac{1}{3}n(n + 12)$. By finding an expression for the $n$$^{th}$ term of the series, show that this is an arithmetic series. Hence, state the common difference of the arithmetic series.[4]

Accepted Answer

(a) $n=13$ (b) First negative term $=-0.5$, sum of all positive terms $=333833.5$ (c) $T_n=\dfrac{2n+11}{3}$, common difference $=\dfrac23$

2024 MI PRU2 P1 Q12

2024 MI PRU2 P1 Q12

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