SOLUTION: if 7 times the seventh term of an A.P.is equal to 11 times the eleventh term,show that the 18th term of an A.P. is zero
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Question 1013416: if 7 times the seventh term of an A.P.is equal to 11 times the eleventh term,show that the 18th term of an A.P. is zero Found 2 solutions by ikleyn, MathTherapy:Answer by ikleyn(52878) (Show Source):
You can put this solution on YOUR website! .
if 7 times the seventh term of an A.P.is equal to 11 times the eleventh term,show that the 18th term of an A.P. is zero
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We have
=
It is true for any AP. You can easily check it yourself. Next, according to the condition,
= .
Simplify:
= , or
= , or
= .
It implies
= 0.
Now notice that = . You can check it yourself.
Thus we conclude that
= 0.
It is what has to be proved.
You can put this solution on YOUR website!
if 7 times the seventh term of an A.P.is equal to 11 times the eleventh term,show that the 18th term of an A.P. is zero
7th term: 11th term:
We then get: ------ Equating 7 times to 11 times _______ 18th term: ------ Substituting - 17d for (PROVEN)
