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यदि समांतर श्रेढ़ी के प्रथम n पदों का योग \((4n^2 + 2n)\) है तो समांतर श्रेढ़ी का सार्व अंतर होगा

(A) 6

(B) 14

(C) 8

(D) 4

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सही विकल्प है (C) 8

माना 'a' प्रथम पद है और 'd' सार्व अंतर है।

यह दिया गया है कि समांतर श्रेढ़ी के प्रथम n पदों का योग \(4 n^2+2 n\) है।

\(\therefore\) प्रथम पद (a) = \(S_1= 4(1)^2+2(1)=4+2=6\)

प्रथम दो पदों का योग \(=S_2=4(2)^2+2(2)=16+4=20\)

\(\therefore\) दूसरा पद \(=S_2-S_1=20-6=14\)

\(\therefore\) सार्व अंतर (d) = दूसरा पद - प्रथम पद

\(= 14 - 6\)

\(= 8\)

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