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यदि किसी समान्तर श्रेणी के n पदों का योगफल `pn+qn^(2)` हो, (जहाँ p व q अचर हैं), तब सार्वअन्तर ज्ञात कीजिए |

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माना, `" "S_(n)=pn+qn^(2)" "`......(i)
`rArr " "S_(n-1)=p(n-1)+q(n-1)^(2)" "`....(ii)
`:. " "a_(n)=S_(n)-S_(n-1)`
`=(pn+qn^(2))-{(n-1)+q(n-1)^(2)}`
`=2qn+(p-q)`
`rArr " " a_(n)=2an+(p-q)" "`......(iii)
`rArr " "a_(n-1)=2q(n-1)+(p-q)" "`.....(iv)
इसलिए `a_(n)-a_(n-1)=2q`, जो कि एक अचर है |
अतः सार्वअन्तर =2q
`rArr` दी गयी समान्तर श्रेणी का सार्वअन्तर 2a है |

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