6 A geometric series has third term 36 and sixth term 972.
- Show that the common ratio of the series is 3 .
- Find the first term of the series.
- The \(n\)th term of the series is \(u _ { n }\).
- Show that \(\sum _ { n = 1 } ^ { 20 } u _ { n } = 2 \left( 3 ^ { 20 } - 1 \right)\).
- Find the least value of \(n\) such that \(u _ { n } > 4 \times 10 ^ { 15 }\).
\(7 \quad\) A curve \(C\) is defined for \(x > 0\) by the equation \(y = x + 3 + \frac { 8 } { x ^ { 4 } }\) and is sketched below.
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