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CORNELIUS GORESEB HIGH SCHOOL MATHEMATICS ~ Sequences, Series and Binomial Theorem TEST 2 10 June 2021 GRADE: 12 AS MARKS: 25 NAME: ……………………………………………… 1. The first 2 terms of a convergent geometric series are 𝑥 and 6 respectively. The sum to infinity is 25. Determine the possible non-zero values of 𝑥. Answer: ……………………………………….[5] Page | 1 2. Given that ∑𝑛𝑟=1 3(2 ) =378 Find the value of 𝑛. Answer: ……………………………………….[5] 3. (a) In the expansion of (3𝑥 − 4)4 , find the coefficient of 𝑥. Answer: ……………………………………….[3] Page | 2 (b) Find the first four terms in the expansion in ascending powers of 𝑥 of (3 + 2𝑥²)10 . Answer: ……………………………………….[4] (c) Find the coefficient of 𝑥³ in the expansions 1 15 (3𝑥² + 𝑥) . Answer: ……………………………………….[3] Page | 3 4. The expansion of (𝑎 + 𝑥)(1 − 3𝑥) in ascending powers of 𝑥 is 4 − 95𝑥 + 𝑝𝑥 2 + ⋯, where 𝑎 and 𝑝 are constants and 𝑛 is a positive integer. Find the values of 𝑎 , 𝑛 and 𝑝. Answer: 𝑎 = ………… 𝑛 = …………. 𝑝 = ……………[5] ……………………………………..end…………………………………………….. Page | 4