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Is the sequence (3)/(2), (1)/(2), - (1)/...

Is the sequence `(3)/(2), (1)/(2), - (1)/(2) , - (3)/(2) , ... ` an A.P.? Justify

Text Solution

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The correct Answer is:
The given sequence is an A.P.
Here, `t_(1) = (3)/(2), t_(2) = (1)/(2), t_(3) = - (1)/(2)`
`t_(4) = - (3)/(2),….`
`t_(2) - t_(1) - (1)/(2) - (3)/(2) =(1-3)/(2) = ( - 2)/(2) = -1 `
`t_(3) - t_(2) = - (1)/(2) - (1)/(2) = ( - 1-1)/(2) = ( - 2)/(2) = - 1 `
` t_(4) - t_(3) = - (3)/(2)- (-(1)/(2)) = - (3)/(2) + (1)/(2) = ( - 3+1)/(2) = ( -2)/(2) = -1`
The common difference between any two consecutive terms `( d= - 1)` is constant
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Knowledge Check

  • STATEMENT-1 : The sum of reciprocals of first n terms of the series 1 + (1)/(3) + (1)/(5) + (1)/(7) + (1)/(9) + … "is" n^(2) and STATEMENT-2 : A sequence is said to be H.P. if the reciprocals of its terms are in A.P.

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    Statemant-1 is True , Statement-2 is True, Statement -2 is NOT a correct explanation for Statement-1
    C
    Statement-1 is True, Stetement-2 is False.
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    Statement-1 is False, Statement-2 is True

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