1.

If`(5+9+13+....to n terms)/(7+9+11+....to(n+1) terms)=17/16`, then `n=`

Answer» Let `S_1 = 5+9+13+...to n` terms
`=>S_1 = n/2(2*5+(n-1)4) = n/2(6+4n) = n(3+2n)`
Let `S_2 = 7+9+11+...to (n+1)` terms
`=>S_2 = (n+1)/2(2*7+(n+1-1)2) = (n+1)/2(14+2n)= (n+1)(7+n)`
So, `S_1/S_2 = 17/16`
`:. (n(3+2n))/((n+1)(n+7)) = 17/16`
`=>16n(3+2n) = 17(n+1)(n+7)`
`=>48n+32n^2 = 17(n^2+8n+7)`
`=>48n+32n^2 = 17n^2+136n+119`
`=>15n^2-88n-119 = 0`
`=>15n^2-105n+17n+119 = 0`
`=>15n(n-7)+17(n-7) = 0`
`=>(15n+17)(n-7) = 0`
`=>n = -15/17 or n = 7`
As `n gt 0`,
`:. n = 7.`


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