If three consecutive terms in an AP are (1)/(a), (1)/(b), (1)/(c), then (b-c)/(a-b)= (a) (a)/(c)

step 1 In this problem, the given series is 1 by A, 1 by B, 1 by C. We have to write the value of first

If three consecutive terms in an AP are (1)/(a), (1)/(b),...

If three consecutive terms in an AP are $\frac{1}{a}, \frac{1}{b}, \frac{1}{c}$, then $\frac{b-c}{a-b}=$
(a) $\frac{\mathrm{a}}{\mathrm{c}}$
(b) $\frac{\mathrm{b}}{\mathrm{a}}$
(c) a
(d) $\frac{c}{a}$

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Key Concepts

Arithmetic Progression

An arithmetic progression (AP) is a sequence of numbers where the difference between any two successive members is constant. This concept underlies many problems in algebra and number theory, as it provides a systematic way to relate and deduce properties of sequential elements in the sequence.

Reciprocal Relationships in Sequences

When sequence terms are given as reciprocals, it introduces an extra layer of complexity as the arithmetic properties must be translated through inverse relationships. Understanding how to work with reciprocal expressions is crucial for setting up equations that relate the sequence's structure to its algebraic properties.

Algebraic Manipulation

Algebraic techniques such as clearing denominators, cross-multiplying, and simplifying expressions are essential for solving equations derived from sequences. Mastery of these methods allows one to transform complex relationships into simpler forms, making it easier to isolate and compare the desired variables.

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