Let a k and b k,k N, be two G.P.s with common ratios r₁ and r₂ respectively such that a₁ = b₁ = 4 and r₁ < r₂. Let c k = a k + b k,k N. If c₂ = 5 and c₃ = 13/4 then Σ k = 1 ^∞ c k - (12a₆ + 8b₄) is equal to _ _ _ _ _.

Sequence and Series: JEE Main 2023 Mathematics question

JEE Main 2023 · 29 Jan, Evening shift · Q49

JEE Main 202329 Jan, Evening shiftMathematicsMediumSequence and Series179× since 2002

Let

\{ {a_k}\}

and

\{ {b_k}\} ,k \in N

, be two G.P.s with common ratios

{r_1}

and

{r_2}

respectively such that

{a_1} = {b_1} = 4

and

{r_1} < {r_2}

. Let

{c_k} = {a_k} + {b_k},k \in N

. If

{c_2} = 5

and

{c_3} = {{13} \over 4}

then

\sum\limits_{k = 1}^\infty {{c_k} - (12{a_6} + 8{b_4})}

is equal to __________.

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