Q13 of 176 Page 20

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

As a,b,c are in GP

Note:

1. In general, the GP series is like a,ar,ar²……….

2. In this, b = ar and c = br = ar²

So we proceed forward with the aim to equalize LHS and RHS of the equation to be proved using the above ideas.

L.H.S =

⇒ LHS =

Now

R.H.S =

⇒ RHS =

∴ RHS = 1/r

Clearly we observed that,

LHS = RHS = (1/r) …Proved

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

(a² + b² + c²), (ab + bc + cd), (b² + c² + d²) are in G.P.

If (a – b), (b – c), (c – a) are in G.P., then prove that (a + b + c)² = 3(ab + bc + ca)

If the 4^th, 10^th and 16^thterms of a G.P. are x, y and z respectively. Prove that x, y, z are in G.P.

If a, b, c are in A.P. and a, b, d are in G.P., then prove that a, a – b, d – c are in G.P.