Q6 of 167 Page 19

If are in A.P., prove that a, b, c are in A.P.

Since are in A.P

Also are also in AP

Therefore,

= are in AP

Multiply by abc in numerator in all terms,

= are in AP

= a, b, c are in AP

Hence proved

If a, b, c are in A.P., prove that:

a² + c² + 4ac = 2 (ab + bc + ca)

If a, b, c are in A.P., prove that:

a³ + c³ + 6abc = 8b³

Show that x² + xy + y², z² + zx + x² and y² + yz + z² are in consecutive terms of an A.P., if x, y and z are in A.P.

Find the A.M. between:

(i) 7 and 13 (ii) 12 and - 8 (iii) (x - y) and (x + y)