1a,1b and 1c are in A.P. Show that : bc, ca and ab are also in A.P. - Mathematics

`1/a, 1/b` and `1/c` are in A.P. Show that : bc, ca and ab are also in A.P.

Sum

Since, `1/a, 1/b` and `1/c` are in A.P.

We have to show that

bc, ca and ab are also in A.P.

∵ `1/a, 1/b` and `1/c` are in A.P.

∴ `2/b = 1/a + 1/c`

`\implies 2/b = (c + a)/(ac)`

`\implies` 2ac = bc + ab or ab + bc

∴ ab, ac and bc are in A.P.

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Simple Applications of Arithmetic Progression

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Chapter 10: Arithmetic Progression - Exercise 10 (D) [Page 146]

Chapter 10 Arithmetic Progression
Exercise 10 (D) | Q 11 | Page 146

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