Question
Download Solution PDFकिसी AP के (p + q)वें और (p – q)वें पदों का योगफल बराबर है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFधारणा:
AP का nवां पद निम्न द्वारा दिया गया है: Tn = a + (n - 1) × d, जहाँ a = पहला पद और d = सार्व अंतर।
गणना:
जैसा कि हम जानते हैं कि, AP का nवां पद निम्न द्वारा दिया गया है: Tn = a + (n - 1) × d, जहाँ a = पहला पद और d = सार्व अंतर।
माना कि a पहला पद है और d सार्व अंतर है।
\(\Rightarrow \;{a_{p + q}} = a + \left( {p + q - 1} \right) \times d\) ...1)
\(\Rightarrow \;{a_{p - q}} = a + \left( {p - q - 1} \right) \times d\) ...2)
(1) और (2) को जोड़कर हम प्राप्त करते हैं
\(\Rightarrow \;{a_{p + q}} + {a_{p - q}} = 2\;a + 2\;\left( {p - 1} \right)d = 2 \times \left[ {a + \left( {p - 1} \right)d} \right] = 2 \times {a_p}\)Last updated on May 30, 2025
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