Question

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

Answer 1

$n^{th}$ term $T_n=2n-1$ ………..$\left(1\right)$

but $T_n=a+(n-1)d$ ……….$\left(2\right)$

$\Rightarrow 2n-1=a+(n-1)d$ (from $\left(1\right)$ & $\left(2\right)$)

$\Rightarrow 2n-1=dn+(a-d)$

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 $19$.