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Question

If 9th term of an A.P. is zero, prove that its 29th term is double the 19th term.

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Solution

Let the first term of an AP = a
and common difference = d
Given: 9th term of an AP is 0.Therefore,
a plus left parenthesis 9 minus 1 right parenthesis d equals 0 rightwards double arrow a plus 8 d equals 0 T o space p r o v e colon space a subscript 29 equals 2 a subscript 19 T h u s comma a subscript 19 equals a plus left parenthesis 19 minus 1 right parenthesis d space space space space space space equals a plus 18 d space space space space space space equals negative 8 d plus 18 d space space space space space space space space space space space left parenthesis sin c e space a equals negative 8 d right parenthesis space space space space space space equals 10 d space space space..... space i right parenthesis A n d a subscript 29 equals a plus left parenthesis 29 minus 1 right parenthesis d space space space space space space equals a plus 28 d space space space space space space equals negative 8 d plus 28 d space space space space space space equals 20 d space space space.... space i i right parenthesis F r o m space i right parenthesis space a n d space i i right parenthesis a subscript 29 equals 2 a subscript 19
Hence proved.

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