NIMCET 2019
If a, b, c are in GP and , and are in AP, then a, b, c are the lengths of the sides of a triangle which is
Answer (Detailed Solution Below)View answer ▾Hide ▴
Answer: Option B — Obtuse angled
Detailed Solution
AP condition: , so .
GP: . So .
Largest side 9: , so the triangle is obtuse angled.
✓ Check
, so the triangle exists, and confirms the GP.⚠ Common trap
(A) acute angled would need ; the triangle inequality alone does not decide the angle.Quick tip
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Arithmetic & Geometric Progression — Preparation
This question tests your understanding of Arithmetic & Geometric Progression, a key topic in the Quantitative Aptitude section. The detailed solution above uses a step-by-step approach to show the reasoning, and where available, a shortcut that helps you solve similar questions in under 90 seconds during the actual exam.
An arithmetic progression (AP) is a sequence where each term differs from the previous one by a constant amount, the common difference. A geometric progression (GP) is a sequence where each term is the previous one multiplied by a constant, the common ratio. This topic covers the nth term and sum of n terms of an AP and GP, the sum of an infinite GP, arithmetic and geometric means, and word problems. Key formulas are the AP nth term a + (n - 1)d, the AP sum n/2 [2a + (n - 1)d], the GP nth term ar^(n-1), and the infinite GP sum a/(1 - r) for |r| < 1. A useful trick is to choose symmetric terms, such as a - d, a, a + d for three terms of an AP, which simplifies many questions. Practise the AP and GP questions below, each with a step-by-step solution.