The sum of the intercepts cut off by the axes on lines $x + y = a, x + y = a r, x + y = a r^{2}, . . . . . . . .$ where $a \neq 0$ and $r = \frac{1}{2}$

2 a

No worries! We‘ve got your back. Try BYJU‘S free classes today!

a \sqrt{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

4 a

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

a

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is D $4 a$
We have,
$x + y = a; x + y = a r; x + y = a r^{2}$
$\frac{x}{a} + \frac{y}{a} = 1; \frac{x}{a r} + \frac{y}{a r} = 1; \dots$
Sum of intercept = $2 a + 2 a r + 2 a r^{2} + \dots$
$\Rightarrow 2 a (1 + r + r^{2} + \dots)$
As it is the sum of infinite GP, the equation reduces to
$\Rightarrow 2 a (\frac{1}{1 - r})$
Putting $r = \frac{1}{2}$
$2 a ⎛ ⎝ \frac{1}{1 - \frac{1}{2}} ⎞ ⎠ = 4 a$

Suggest Corrections

Similar questions

Q. The sum of the intercepts cut off by the axes on the lines

x + y = a, x + y = a r, x + y = a r^{2} \dots \dots \dots

where

a \neq 0

and

r = \frac{1}{2}

Q. The sum of the intercepts cut off by the axes on the lines

x + y = a, x + y = a r, x + y = a r^{2} \dots \dots \dots

where

a \neq 0

and

r = \frac{1}{2}

For what values of a a and b the intercepts cut off on the coordinate axes by the line ax + by + 8 = 0 are equal in length but opposite in signs to those cut off by the line 2x - 3y + 6 = 0 on the axes.

Q. Find the intercepts cut off by the line

x + y - 1 = 0

on the axes.

Q. For what values of

a

and

b

the intercepts cut off on the coordinate axes by the line

a x + b y + 8 = 0

are equal in length but opposite in signs to those cut off by the line

2 x - 3 y + 6 = 0

on the axis.

Join BYJU'S Learning Program

The sum of the intercepts cut off by the axes on lines x+y=a, x+y=ar, x+y=ar2,........ where a≠0 and r=12

The correct option is D 4aWe have,x+y=a;x+y=ar;x+y=ar2xa+ya=1;xar+yar=1;…Sum of intercept = 2a+2ar+2ar2+⋯⇒2a(1+r+r2+⋯)As it is the sum of infinite GP, the equation reduces to⇒2a(11−r)Putting r=122a⎛⎝11−12⎞⎠=4a

The sum of the intercepts cut off by the axes on lines $x + y = a, x + y = a r, x + y = a r^{2}, . . . . . . . .$ where $a \neq 0$ and $r = \frac{1}{2}$