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If for sequence lt a_n gtsum of n terms S_n= 2n^2+3n then find the sum {:(""Sigma Sigma),(1lei lt j le 10):}a_ia_j

Answer» <html><body><p><br/></p>Solution :We have `S_(<a href="https://interviewquestions.tuteehub.com/tag/n-568463" style="font-weight:bold;" target="_blank" title="Click to know more about N">N</a>)=2n^(<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>)+<a href="https://interviewquestions.tuteehub.com/tag/3n-310768" style="font-weight:bold;" target="_blank" title="Click to know more about 3N">3N</a>` <br/> `thereforea_(n)=S_(n)-S_(n-1)` <br/> `=2n^(2)+3n-2(n-1)^(2)-3(n-1)` <br/> =4n+1 <br/> Therefore, the sequence is 5,9,13… <br/> `thereforeunderset(1leiltjle10)(SigmaSigma)a_(i)a_(<a href="https://interviewquestions.tuteehub.com/tag/j-520843" style="font-weight:bold;" target="_blank" title="Click to know more about J">J</a>)=(sum_(i=1)^(<a href="https://interviewquestions.tuteehub.com/tag/10-261113" style="font-weight:bold;" target="_blank" title="Click to know more about 10">10</a>)sum_(j=1)^(10)(4i+1)cdot(4j+1)-sum_(i=1)^(10)(4i+1)^(2))/2` <br/> `=((sum_(i=1)^(10)(4i+1))^(2)-sum_(i=1)^(10)(4i+1)^(2))/2` <br/> =23145</body></html>


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