In a G.P. of positive terms, if any term is equal to the sum of the next two terms. Then the common ratio of the G.P. is
Mastering sequences and series is essential for excelling in mathematics, and the CBSE 2024-2025 NCERT Class 11th syllabus ensures a structured approach to learning these concepts. This chapter delves into arithmetic and geometric progressions, covering fundamental formulas such as the nth term, sum of n terms, arithmetic mean, and geometric mean. To strengthen conceptual understanding, multiple-choice questions are provided, allowing students to test their knowledge and improve problem-solving speed. Regular practice of these MCQs enhances logical reasoning, helping students build confidence for board exams and competitive tests. A solid grasp of sequences and series not only aids in academic success but also develops critical thinking skills for tackling advanced mathematical challenges.
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Choice (d) is correct.
Let a and r be the first term and the common ratio of the G.P.
Given, any term of the G.P. is equal to the sum of the next two terms.
Tₙ = Tₙ ₊ ₁ + Tₙ ₊ ₂ ⇒ arⁿ ⁻ ¹ = arⁿ + arⁿ ⁺ ¹ ⇒ 1 = r + r²
⇒ r² + r – 1 = 0
⇒ r = -1 ±√ 1² – 4 × 1 × (-1)/ 2 × 1 = -1 ± √5/2
⇒ r =√5 – 1/2
⇒ r = 2( √5 – 1/2) = 2 sin 18°
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