Moderate -0.8 Part (a) is a straightforward application of the sum to infinity formula S∞ = a/(1-r), requiring simple algebraic manipulation to find r. Part (b) requires setting up and solving S_n > 300 using the finite sum formula, then finding the smallest integer n, which involves logarithms but is still a standard textbook exercise with no novel insight required.
3. The first term of a geometric series is 120 . The sum to infinity of the series is 480 .
a) Show that the common ratio, \(r\), is \(\frac { 3 } { 4 }\)
The sum of the first n terms of the series is greater than 300 .
b) Calculate the smallest possible value of n [0pt]
3. The first term of a geometric series is 120 . The sum to infinity of the series is 480 .\\
a) Show that the common ratio, $r$, is $\frac { 3 } { 4 }$
The sum of the first n terms of the series is greater than 300 .\\
b) Calculate the smallest possible value of n\\[0pt]
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\hfill \mbox{\textit{SPS SPS FM 2022 Q3 [5]}}