, , and are consecutive terms of an arithmetic sequence. Prove that the following are…

MATHEMATICS · Multi-part · CBSE · Mathematics · Arithmetic Progressions · Arithmetic Progressions

Problem

a

b

, and

c

are consecutive terms of an arithmetic sequence. Prove that the following are also consecutive terms of an arithmetic sequence: (1)

b + c

c + a

, and

a + b

(2)

\frac{1}{\sqrt{b} + \sqrt{c}}

\frac{1}{\sqrt{c} + \sqrt{a}}

, and

\frac{1}{\sqrt{a} + \sqrt{b}}