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Demonstrate the identity `a_(n+1)-a_n = 2` if `a_(n)=2n+3` ?

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yapayapa | Honors

Posted September 22, 2013 at 4:49 PM via web

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Demonstrate the identity `a_(n+1)-a_n = 2` if `a_(n)=2n+3` ?

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted September 22, 2013 at 4:58 PM (Answer #1)

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It is given that `a_n = 2n + 3`

The identity `a_(n+1) - a_n = 2` has to be proved.

`a_(n+1) - a_n`

= `2(n + 1) + 3 - (2n + 3)`

= 2n + 2 + 3 - 2n - 3

=> 2

This proves that `a_(n+1) - a_n = 2` if `a_n = 2n + 3`

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