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Let a1,a2,a3 ...... a11 be real numbers ...

Let a1,a2,a3 ...... a11 be real numbers satisfying `a_1 =15, 27-2a_2 > 0 and a_k= 2a_(k-1) - a_(k-2)` for `k=3,4,.....11` If `(a1^2 +a2^2.......a11^2)/11 = 90` then find the value of `(a_1+a_2....+a_11)/11`

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`a_k=2a_(k-1)-a_(k-2)rArr a_1,a_2rArr a_1,a_2,.....a_(11)` are in A.P
`therefore (a_(1)^2+a_(2)^2+….+a_11^2)/(11)=(11a^2+35xx11d^2+110ad)/11=90`
`rArr 225+35d^2+150d^2+150d=90`
`35d^2+150d+135=0 rArr -3,-9//7`
`a_2 lt (27)/(2),` we get d= -3 and `d=-9//7`
`rArr (a_(1)+a_2+....+a_11)/(11)=11/2[30-10xx3]=0`
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