Question
Download Solution PDFसमांतर श्रेणी -10, -7, -4, .... के प्रथम k पदों का योग 104 है। \(\frac{k+9}{k-5}\) का मान क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
समांतर श्रेणी: -10, -7, -4, ...
प्रथम k पदों का योग (Sk) = 104
प्रयुक्त सूत्र:
Sk = (k/2)[2a + (k - 1)d]
जहाँ a पहला पद है और d सार्व अंतर है।
गणना:
a = -10
d = -7 - (-10) = 3
अब, मानों को योग सूत्र में प्रतिस्थापित कीजिए:
⇒ 104 = (k/2)[2(-10) + (k - 1)3]
⇒ 104 = (k/2)[-20 + 3k - 3]
⇒ 104 = (k/2)[3k - 23]
⇒ 208 = k(3k - 23)
⇒ 3k2 - 23k - 208 = 0
⇒ 3k2 - 39k + 16k - 208 = 0
⇒ 3k(k - 13) + 16(k - 13) = 0
⇒ (3k + 16)(k - 13)
⇒ k = 13, या -16/3(ऋणात्मक संभव नहीं है)
(k + 9) / (k - 5) का मान है:
⇒ (13 + 9) / (13 - 5) = 22/8 = 11/4.
इसलिए सही उत्तर 11/4 है।
Last updated on Apr 24, 2025
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