Which of the following sequences are A.P.? If they are A.P. find the common difference. i) 0.3, 0.33, 0.333, … ii) 0, -4, -8, -1

Question

Which of the following sequences are A.P.? If they are A.P. find the common difference.
i) 0.3, 0.33, 0.333, …
ii) 0, -4, -8, -12

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Jade 3 weeks 2021-11-07T00:41:19+00:00 1 Answer 0 views 0

Answers ( )

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    2021-11-07T00:42:45+00:00

     i )Given \: sequence : 0.3,0.33,0.333, \ldots

     First \: term (a_{1} ) = a = 0.3

     Second\: term (a_{2} ) = 0.33

     Third \: term (a_{3} ) = 0.333

     a_{2} - a_{1} = 0.33 - 0.3 = 0.03

     a_{3} - a_{2} = 0.333 - 0.33 = 0.003

     \therefore a_{2} - a_{1}\pink { \neq} a_{3} - a_{2}

     \red{ So, given \: series \: is \: not \: in \: A.P .,}

     ii )Given \: sequence : 0,-4,-8,-12, \ldots

     First \: term (a_{1} ) = a = 0

     Second\: term (a_{2} ) = -4

     Third \: term (a_{3} ) = -8

     a_{2} - a_{1} = -4  - 0= -4

     a_{3} - a_{2} = -8 - (-4) = -8 + 4= -4

     \therefore a_{2} - a_{1}\pink { =} a_{3} - a_{2}

     \green{ So, given \: series \: is  \: in \: A.P .,}

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