A-LevelMathematicsSeries9709/12 · Oct/Nov 2021 · Q65 Marks
The second term of a geometric progression is 54 and the sum to infinity of the progression is 243. The common ratio is greater than ¹/₂. Find the tenth term, giving your answer in exact form.
- The second term of a geometric progression is 54 and the sum to infinity of the progression is 243. The common ratio is greater than ¹/₂. Find the tenth term, giving your answer in exact form.[5]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2021). The mark or mark type is shown in brackets.
- [B1] ar = 54 and a/(1-r) = 243 SOI
- [*M1] Forming a 3-term quadratic expression in r or a using their 2nd term and S∞. Allow ± sign errors.
- [DM1] Solving their 3-term quadratic using factorisation, formula or completing the square. If factorising, factors must expand to give ±their coefficient of r².
- [DM1] May be implied by final answer.
- [A1] Tenth term = 512/3 OE. Must be exact.
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