Question 1013416
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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 

{{{a[11]}}} = {{{a[7]+4d}}}

It is true for any AP. You can easily check it yourself. Next, according to the condition,

{{{7*a[7]}}} = {{{11*(a[7]+4d)}}}.

Simplify:

{{{0}}} = {{{(11-7)*a[7] + 44d}}},   or

{{{0}}}= {{{4*a[7] + 44d}}},   or

{{{0}}}= {{{4*(a[7] + 11d)}}}.

It implies 

{{{a[7] + 11d}}} = 0.

Now notice that {{{a[7] + 11d}}} = {{{a[18]}}}. You can check it yourself.

Thus we conclude that

{{{a[18]}}} = 0.

It is what has to be proved.
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