1.

If the 9th term of an A.P. is zero then show that the 29th term is twice the 19th term.​

Answer»

Solution :

LET a and d be the FIRST term and common DIFFERENCE of the AP

Since,

\sf a_9 = 0 \\ \\ \leadsto \sf a + 8D = 0 \\ \\ \leadsto \boxed{\boxed{\sf{a = - 8D}}}

\rule{300}{2}

\sf a_{29} = a + 28D \\ \\ \leadsto \sf a_{29} = - 8D + 28D \\ \\ \leadsto \sf a_{29} = 20D

\rule{300}{2}

\sf a_{19} = a + 18D \\ \\ \leadsto \sf a_{19} = - 8D + 18D \\ \\ \leadsto \sf a_{19} = 10 D

Since,

\sf a_{29} = 2a_{19}

HENCE,PROVED


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