Question

# The $$n^{th}$$ term of an A.P. is given by $$Tn = 2n-1.$$ Then $$10^{th}$$ term of the A.P. is _____________.

Solution

## $$n^{th}$$ term $$T_n=2n-1$$ ………..$$(1)$$but $$T_n=a+(n-1)d$$ ……….$$(2)$$$$\Rightarrow 2n-1=a+(n-1)d$$      (from $$(1)$$ & $$(2)$$)$$\Rightarrow 2n-1=dn+(a-d)$$On comparing constant terms and coefficient of 'n'We get $$d=2$$ and $$(a-d)=-1$$$$\Rightarrow (a-2)=-1$$$$\Rightarrow a=1$$$$\therefore$$ first term $$=1$$and common difference $$=d=2$$$$\therefore 10^{th}$$ term $$=a+(10-1)d=a+9d$$$$=1+9\times 2=19$$$$\therefore 10^{th}$$ term of the AP is $$19$$.Mathematics

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