Question
Download Solution PDFयदि किसी समान्तर श्रेणी के प्रथम 9 पदों के योग का प्रथम 15 पदों के योग से अनुपात 9 : 25 है, तो 9वें पद का 15वें पद से अनुपात क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
किसी समान्तर श्रेणी के प्रथम 9 पदों के योग का प्रथम 15 पदों के योग से अनुपात 9 : 25 है।
प्रयुक्त सूत्र:
समान्तर श्रेणी के प्रथम n पदों का योग: Sn = n/2 [2a + (n-1)d]
गणना:
S9 = 9/2 [2a + 8d]
S15 = 15/2 [2a + 14d]
दिया गया है कि, S9 / S15 = 9/25
⇒ (9/2 [2a + 8d]) / (15/2 [2a + 14d]) = 9/25
⇒ (9 [2a + 8d]) / (15 [2a + 14d]) = 9/25
⇒ (2a + 8d) / (2a + 14d) = 3/5
⇒ 10a + 40d = 6a + 42d
⇒ 4a = 2d
⇒ a = d/2
9वाँ पद (T9) = a + 8d = (d/2 + 8d) = 17d/2
15वाँ पद (T15) = a + 14d = (d/2 + 14d) = 29d/2
⇒ T9 / T15 = (17d/2) / (29d/2)
⇒ 17 / 29
∴ सही उत्तर विकल्प (3) है।
Last updated on Apr 24, 2025
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