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Question Number 140462 by ZiYangLee last updated on 08/May/21

Commented by mr W last updated on 08/May/21

T_n =ar^(n−1) ((T_(n+4) −T_(n+2) )/T_(n+1) )=((ar^(n+3) −ar^(n+1) )/(ar^n ))=r^3 −r =(r−1)r(r+1) one of r and r+1 is even, so (r−1)r(r+1) is always even.

Tn=arn−1Tn+4−Tn+2Tn+1=arn+3−arn+1arn=r3−r=(r−1)r(r+1)oneofrandr+1iseven,so(r−1)r(r+1)isalwayseven.

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