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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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