Question
Download Solution PDFयदि दो समांतर श्रेणियों के nवें पद 3n + 8 और 7n + 15 हैं तब इनके 12वें पदों का अनुपात क्या होगा?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFअवधारणा:
यदि a समांतर श्रेणी का पहला पद है और d सार्व अंतर है तो
एक समांतर श्रेणी का nवां निम्न द्वारा दिया जाता है :
an = a + (n - 1) × d
गणना:
दिया हुआ: दो समांतर श्रेणियों के nवें पद 3n + 8 और 7n + 15 हैं।
यहां हमें उनके 12 वें पदों के बीच का अनुपात खोजना होगा।
इसलिए 1ली समांतर श्रेणी में 12वां पद:
(T12)1 = 3 × 12 + 8
⇒ (T12)1 = 36 + 8 = 44
⇒ (T12)1 = 44 ---(1)
उसी प्रकार 2री समांतर श्रेणी का 12वां पद:
⇒ (T12)2 = 7 × 12 + 15
⇒ (T12)2 = 84 + 15 = 99
⇒ (T12)2 = 99 ----(2)
∴ आवश्यक अनुपात = 44/99 = 4/9 = 4 ∶ 9
Last updated on May 26, 2025
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