Question

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

Answer 1

Correct Answer - 23145
We have `S_(n)=2n^(2)+3n`
`thereforea_(n)=S_(n)-S_(n-1)`
`=2n^(2)+3n-2(n-1)^(2)-3(n-1)`
=4n+1
Therefore, the sequence is 5,9,13…
`thereforeunderset(1leiltjle10)(SigmaSigma)a_(i)a_(j)=(sum_(i=1)^(10)sum_(j=1)^(10)(4i+1)cdot(4j+1)-sum_(i=1)^(10)(4i+1)^(2))/2`
`=((sum_(i=1)^(10)(4i+1))^(2)-sum_(i=1)^(10)(4i+1)^(2))/2`
=23145