पुढील आकृतीवरून सहाव्या रचनेत किती त्रिकोण (Δ) येतील ?
योग्य उत्तर पर्याय १ (A) (50) आहे.
महत्त्वाचे मुद्दे (Key Points):
• रचनांमधील त्रिकोणांची संख्या तपासल्यास: रचना १ = ५, रचना २ = १०, रचना ३ = १७.
• या संख्येतील फरक ५, ७, ९, ११, १३ असा विषम संख्यांनी वाढतो.
• त्यामुळे: रचना ४ = १७ + ९ = २६, रचना ५ = २६ + ११ = ३७, रचना ६ = ३७ + १३ = ५० त्रिकोण येतील.
• महत्त्वाची टीप: संख्या श्रेणी: ५, १०, १७, २६, ३७, ५० (फरक: ५, ७, ९, ११, १३ या विषम संख्या).
The correct answer is Option A (50).
Key Points:
• Counting triangles in the given sequence: Arrangement 1 has 5 triangles (1² + 4 or 2² + 1).
• Arrangement 2 has 10 triangles.
• Arrangement 3 has 17 triangles (3² + 8 or n² + extpattern).
• The formula governing n-th arrangement is T_n = (n+1)² + 1 or quadratic progression: T₁ = 5, T₂ = 10, T₃ = 17, T₄ = 26, T₅ = 37, T₆ = 50 (derived as (6+1)² + 1 = 49 + 1 = 50).
• Thus, Option 1 (50) is correct.
• Key Takeaway: Sequence values: 5, 10, 17, 26, 37, 50 (Differences are consecutive odd numbers: 5, 7, 9, 11, 13).
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