Let be a sequence of positive integers in arithmetic progression with common difference 2 . Also, let be a sequence of positive integers in geometric progression with common ratio 2 . If , then the nu...

[As, must be positive integer and as for , not possible] The above inequality holds for . Taking using (i), we get For di...

Let a_{1},a_{2},a_{3}, be a sequence of positive integers in arithmetic progression with common difference 2 . Also, let b_{1},b_{2},b_{3}, be a sequence of positive integers in geometric progression with common ratio 2 . If a_{1} = b_{1} = c, then the number of all possible values of c, for which the equality 2( a_{1} + a_{2} + + a_{n} ) = b_{1} + b_{2} + + b_{n} holds for some positive integer n, is: Sequence & Series (Mathematics)

Let

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

be a sequence of positive integers in arithmetic progression with common difference 2 . Also, let

b_{1},b_{2},b_{3},\ldots

be a sequence of positive integers in geometric progression with common ratio 2 . If

a_{1} = b_{1} = c

, then the number of all possible values of

c

, for which the equality

2\left( a_{1} + a_{2} + \ldots + a_{n} \right) = b_{1} + b_{2} + \ldots + b_{n}

holds for some positive integer

n

, is

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