Let a 1- a 2- a 3- are in G-P and let - n -1100 a 2 n - and - n -1100-2 n -1- such that - - then the common ratio isA-B- 1C- -

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Algebra of Derivatives

Let a 1, a 2,...

Question

Let $a_{1}, a_{2}, a_{3} . . . . . .$ are in G.P and let $\sum_{n = 1}^{100} a_{2 n} = α$ and $\sum_{n = 1}^{100} α_{2 n - 1} = β$ , such that $α \neq β$ , then the common ratio is

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a_{n}

n^{t h}

100 \sum n = 1 a_{2 n} = α

100 \sum n = 1 a_{2 n - 1} = β, α \neq β .

\sum_{n = 1}^{100} a_{2 n} = α and \sum_{n = 1}^{100} a_{2 n - 1} = β,

a_{n}

n^{t h}

G . P .

100 \sum n = 1 a_{2 n} = α

100 \sum n = 1 a_{2 n - 1} = β

α \neq β

G . P .

α, β, γ \neq 0,

∣ ∣ ∣ ∣ \begin{matrix} α + a_{1} b_{1} & a_{1} b_{2} & a_{1} b_{3} a_{2} b_{1} & β + a_{2} b_{2} & a_{2} b_{3} a_{3} b_{1} & a_{3} b_{2} & γ + a_{3} b_{3} \end{matrix} ∣ ∣ ∣ ∣

= α β γ [1 + \frac{a_{1} b_{1}}{α} + \frac{a_{2} b_{2}}{β} + \frac{a_{3} b_{3}}{γ}]

L e t α, β b e s u c h t h a t π < α - β < 3 π . I f s i n α + s i n β = \frac{21}{65} a n d c o s α + c o s β = - \frac{27}{65}, t h e n t h e v a l u e o f c o s \frac{α - β}{2} i s

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