<ol class="abc-list"><li><div class="list-item-paragraph">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 \(\left| S - S_n \right| &lt; 0.001\).<span class="inline-marks">[5]</span></div></li><li><div class="list-item-paragraph">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.<span class="inline-marks">[4]</span></div></li><li><div class="list-item-paragraph">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.<span class="inline-marks">[4]</span></div></li></ol>

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 \(\left| S - S_n \right| < 0.001\).

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.

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.

2024 MI PRU2 P1 Q12

2024 MI PRU2 P1 Q12