जर a, b, c हे अंकगणिती श्रेढीमध्ये असतील, तर 3a, 3b, 3c हे               मध्ये असतील.

  1. अंकगणिती श्रेढी 
  2. भूमिती श्रेढी 
  3. हार्मोनिक श्रेढी
  4. यापैकी नाही

Answer (Detailed Solution Below)

Option 2 : भूमिती श्रेढी 
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Detailed Solution

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a, 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.

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