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Per NCERT, in the Sierpiński triangle, what is the AREA of the black region at stage n (starting with area 1 square unit at stage 0)?
Asₙ = (3/4)ⁿ — a GP with common ratio 3/4 (area shrinks each stage)
Bsₙ = 3ⁿ
Csₙ = 1 always
Dsₙ = 4ⁿ
Answer & Solution
Correct answer: A. sₙ = (3/4)ⁿ — a GP with common ratio 3/4 (area shrinks each stage)
Per NCERT §8.6.1 Table 1, at each stage the area becomes 3/4 of the previous stage's area. So sₙ = (3/4)ⁿ.
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