Let a_k and b_k , k N , be two G.P.s with common ratio r₁ and r₂ respectively such that a ₁= b ₁=4 and r ₁

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Let a_k and b_k , k N , be two G.P.s with common ratio r₁ and r₂ respectively such that a ₁= b ₁=4 and r ₁< r ₂ . Let c _ k = a _ k + b _ k , k N . If c ₂=5 and c ₃= 13 4 then _ k =1 ^ c _ k - (12 a ₆+8 ~b ₄ ) is equal to

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Given: c k = a k + b k and a 1 = b 1 = 4 Also, a 2 = 4 r 1 and a 3 = 4 r 1 2 b 2 = 4 r 2 and b 3 = 4 r 2 2 Now, c 2 = a 2 + b 2 = 5 &#8658; 4 r 1 + 4 r 2 = 5 &#8658; r 1 + r 2 = 5 4 And, c 3 = a 3 + b 3 = 13 4 &#8658; r 1 2 + r 2 2 = 13 16 &#8658; r 1 + r 2 2 - 2 r 1 r 2 = 13 16 &#8658; 25 16 - 2 r 1 r 2 = 13 16 &#8658; 2 r 1 r 2 = 12 16 &#8658; r 1 r 2 = 3 8 &#8658; 8 r 1 5 4 - r 1 3 &#8658; 10 r 1 - 8 r 1 2 = 3 &#8658; 8 r 1 2 - 10 r 1 + 3 = 0 &#8658; r 1 = 10 &#177; 100 - 96 16 &#8658; r 1 = 3 4 , &#160; 1 2 &#8

Let a_k and b_k , k N , be two G.P.s with common ratio r₁ and r₂ respectively such that a ₁= b ₁=4 and r ₁< r ₂ . Let c _ k = a _ k + b _ k , k N . If c ₂=5 and c ₃= 13 4 then _ k =1 ^ c _ k - (12 a ₆+8 ~b ₄ ) is equal to

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