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Sequences and Series question

2024 · 6 Apr · Shift 2 · Q41

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JEE Main
Mathematics
Sequences and Series
2024 · 6 Apr · Shift 2 · Q41

Sequences and Series question

2024 · 6 Apr · Shift 2 · Q41

JEE MainMathematicsSequences and SeriesMCQ+4 / −1

Let

A B C

be an equilateral triangle. A new triangle is formed by joining the middle points of all sides of the triangle

A B C

and the same process is repeated infinitely many times. If

\mathrm{P}

is the sum of perimeters and

Q

is be the sum of areas of all the triangles formed in this process, then :

A
$\mathrm{P}^2=72 \sqrt{3} \mathrm{Q}$
B
$\mathrm{P}^2=36 \sqrt{3} \mathrm{Q}$
C
$\mathrm{P}=36 \sqrt{3} \mathrm{Q}^2$
D
$\mathrm{P}^2=6 \sqrt{3} \mathrm{Q}$

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