Challenging +1.2 This question requires understanding that equal differences in an arithmetic sequence translate to equal differences of logarithms, leading to a ratio equation. Students must manipulate exponentials and solve a quadratic in 3^k. While it involves multiple steps (using AP property, exponentiating, expanding, and solving), the techniques are standard A-level methods with no novel insight required. It's moderately harder than average due to the algebraic manipulation involved, but remains a recognizable exercise type.
9.
In this question you must show all stages of your working.
Solutions relying on calculator technology are not acceptable.
The first 3 terms of an arithmetic sequence are
$$\ln 3 \quad \ln \left( 3 ^ { k } - 1 \right) \quad \ln \left( 3 ^ { k } + 5 \right)$$
Find the exact value of the constant \(k\). [0pt]
9.
In this question you must show all stages of your working.\\
Solutions relying on calculator technology are not acceptable.\\
The first 3 terms of an arithmetic sequence are
$$\ln 3 \quad \ln \left( 3 ^ { k } - 1 \right) \quad \ln \left( 3 ^ { k } + 5 \right)$$
Find the exact value of the constant $k$.\\[0pt]
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\hfill \mbox{\textit{SPS SPS SM Statistics 2022 Q9 [5]}}