Question

If a, b, c are p^th, q^th and r^th terms of H.P. respectively then prove that bc(q – r) + ca(r – p) + ab(p – q) = 0.

Answer 1

The p^th term of H.P. = a

a^th term = b

r^th term = c

Let first term of corresponding A.P. is x and common difference is y. 

Then p^th term of corresponding

Multiplying equation (i) by (q - r), equation (ii) by (r - p) and equation (iii) by p - q