Question

If a, b, c are in A.P. and |a|, |b|, |c| < 1, and $x = 1 + a + a ^ { 2 } + \ldots \infty$, $y = 1 + b + b ^ { 2 } + \ldots \infty$ , $z = 1 + c + c ^ { 2 } + \ldots \ldots \infty$

Then x, y, z shall be in

• A. A.P.
• B. G.P.
• C. H.P.
• D. None of these

Answer 1

Answer: (C)

H.P.

Answer 2

$x = 1 + a + a ^ { 2 } + \ldots \infty = \frac { 1 } { 1 - a }$

$z = 1 + c + c ^ { 2 } + \ldots . \infty = \frac { 1 } { 1 - c }$

Now, a, b, c are in A.P.

⇒ 1 – a, 1 – b, 1 – c are in A.P.

⇒ $\frac { 1 } { 1 - a } , \frac { 1 } { 1 - b } , \frac { 1 } { 1 - c }$ are in H.P.

Therefore x, y, z are in H.P.