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Let a₁, a₂, a₃, , a₁₁ be real numbers satisfying a₁=15,27-2 a₂>0 and a_k=2 a_ k-1 -a_ k-2 for k=3,4, , 11 . If a₁^2+a₂^2+ +a₁₁^2 11 =90 , then the value of a₁+a₂+ +a₁₁ 11 is equal to

Correct answer

0

Step-by-step solution

aligned & a_k=2 a_ k-1 -a_ k-2 & a₁, a₂, , a₁₁ are in AP & a₁^2+a₂^2+ +a₁₁^2 11 &= 11 a^2+35 11 d^2+10 a d 11 =90 & 225+35 d^2+150 d=90 & 35 d^2+150 d+135=0 & d=-3,- 9 7 aligned Given, a₂ < 27 2 d=-3 and d - 9 7 a₁+a₂+ +a₁₁ 11 = 11 2 [30-10 3]=0

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