Black Book Advanced Problems in MathematicsMathematicsSequences and Series

If ( - 2 ) , , ( + 2 ) are in arithmetical progression then ^2 = ^2 ( n , n I ) the value of is:

Options

A1
B2
C3
D1 2

Correct answer

C. 3

Step-by-step solution

2 = ( - 2 ) + ( + 2 ) 2 = ( + 2 ) + ( - 2 ) ( - 2 ) ( + 2 ) 2 = 2 2 ^2 - ^2 2 Cross-multiplying gives: ^2 - ^2 2 = ^2 2 ^2 (1 - 2 ) = ^2 2 = 1 - ^2 2 = (1 - 2 )(1 + 2 ) Since n , 1 - 2 0 . ^2 = 1 + 2 = 2 ^2 Thus, = 2 .

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