Question

# If $$7th$$ term of $$AP$$ is $$7$$ times is equal to $$11$$ times of $$11th$$term of $$AP$$ the that $$18th$$ term is zero.

Solution

## Given $$7^{th}$$ term of A.P is equal to $$11$$ terms the $$11^{th}$$ term of A.P.Let $$7^{th}$$ term of A.P$$=a+(n-1)d$$$$=a+(7-1)d$$$$=a+6d$$d- common differencea- first term$$11^{th}$$ term of A.P$$=a+(11-1)d$$$$=a+10d$$Given, $$7(a+6d)=11(a+10d)$$$$7a+42d=11a+110d$$$$\Rightarrow 4a=-68d$$$$\Rightarrow a=-17d$$ ………..$$(1)$$$$18^{th}$$ term of A.P$$=a+(18-1)d$$$$=a+17d$$ [From $$(1)$$]$$=-17d+17d$$$$=0$$.Mathematics

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