Question
Download Solution PDFजर a, b, c हे अंकगणिती श्रेढीमध्ये असतील, तर 3a, 3b, 3c हे मध्ये असतील.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFa, b, c हे अंकगणिती श्रेढीमध्ये आहेत.
⇒ b - a = c - b ⇒ 2b = a + c---(1)
जर a, b, c हे भूमिती श्रेढीमध्ये असतील, तर \(b = \sqrt{a\times c}\)
⇒ \({3^b} = \sqrt {{3^a} \times {3^c}} \)
दोन्ही बाजूंचा वर्ग केल्यास, आपल्याकडे,
⇒ \({3^{2b}} = {3^{a + c}}\) ⇒ 2b = a + c -----(2)
समीकरण (1) आणि (2) वरून, आपल्याकडे,
अनुक्रम \({3^a},\;{3^b},\;{3^c}\) ही एक भूमिती श्रेढी आहे.
Last updated on May 26, 2025
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