If a 1 - a 2 - a 3 -5-4- a 6 - a 7 - a 8 - a 9 are in H-P- and D- a 1 a 2 a 3 5 4 a 6 a 7 a 8 a 9- then the value of -D- is where - represents the greatest integer function

Given a _ 1 , a _ 2 , a _ 3 ,5,4, a _ 6 , a _ 7 , a _ 8 , a _ 9 are in H.P. ⇒ a+3d=1/5; a+4d=1/4 where, a,d are first term and common diference ...

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Properties of Determinants

If a 1 , a ...

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If $a_{1}, a_{2}, a_{3}, 5, 4, a_{6}, a_{7}, a_{8}, a_{9}$ are in H.P., and $D = ∣ ∣ ∣ ∣ \begin{matrix} a_{1} & a_{2} & a_{3} 5 & 4 & a_{6} a_{7} & a_{8} & a_{9} \end{matrix} ∣ ∣ ∣ ∣$ , then the value of $[D]$ is (where [.] represents the greatest integer function)

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a_{1}, a_{2}, a_{3}, 5, 4, a_{6}, a_{7}, a_{8}, a_{9}

D = ∣ ∣ ∣ ∣ \begin{matrix} a_{1} & a_{2} & a_{3} 5 & 4 & a_{6} a_{7} & a_{8} & a_{9} \end{matrix} ∣ ∣ ∣ ∣

21 D

A_{1} = [a_{1}] A_{2} = [\begin{matrix} a_{2} & a_{3} a_{4} & a_{5} \end{matrix}] A_{3} = ⎡ ⎢ ⎣ \begin{matrix} a_{6} & a_{7} & a_{8} a_{9} & a_{10} & a_{11} a_{12} & a_{13} & a_{14} \end{matrix} ⎤ ⎥ ⎦ \dots \dots A_{n} = [\dots] where a_{r} = [{log}_{2} r]

([\cdot]

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A_{10}

a_{1}, a_{2}, a_{3}, \dots \dots

a_{3} + a_{5} + a_{8} = 11

a_{4} + a_{2} = - 2

a_{1} + a_{6} + a_{7}

{(1 + x)}^{10} = a_{0} + a_{1} x + a_{2} x^{2} + . . . . . . a_{10} x^{10}

{(a_{0} - a_{2} + a_{4} - a_{6} + a_{8} - a_{10})}^{2} + {(a_{1} - a_{3} + a_{5} - a_{7} + a_{9})}^{2}

(1 + x)^{10} = a_{0} + a_{1} x + a_{2} x^{2} + . . . . . + a_{10} x^{10}

(a_{0} - a_{2} + a_{4} - a_{6} + a_{8} - a_{10})^{2} + (a_{1} - a_{3} + a_{5} - a_{7} + a_{9})^{2}

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