If x, 2y, 3z are in A.P. where the distinct numbers x, y, z are in G.P., then the common ratio of the G.P. is
The CBSE 2024-2025 NCERT Class 11th syllabus introduces students to sequences and series which are essential for understanding mathematical patterns and solving complex problems. This chapter covers arithmetic and geometric progressions along with important concepts like the nth term sum of n terms arithmetic mean geometric mean and special series. Multiple-choice questions are included to help students test their knowledge and improve their accuracy. Regular practice of these MCQs enhances logical reasoning and boosts confidence for exams. A strong understanding of sequences and series is crucial not only for scoring well in board exams but also for excelling in competitive exams and higher mathematical studies.
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Choice (c) is correct.
Since x, 2y, 3z are in A.P.
2y = x + 3z/ 2⇒ 4y = x + 3z
Again, x, y, z are in G.P.
Let r be its common ratio.
y = xr and z = yr = (xr)r = xr²
Putting values of y and z from (2) in (1), we get
4xr = x +3xr² ⇒ 3r² – 4r + 1 = 0 ⇒ 3r² – 3r – r + 1= 0
⇒ 3r(r – 1) – (r – 1) = 0 ⇒ (r – 1)(3r – 1) = 0 ⇒ r = 1 or r = 1/3
r = 1/3
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