Question

Find${}^{\prime }{k}^{\prime }$ if given value of$x$ is the $k^{th}$ term of the $A.P$ $5\frac{1}{2},11,16\frac{1}{2},\mathrm{22..........},x=550$

Answer 1

We can see that First term $a=5\frac{1}{2}=\frac{11}{2}$

and common difference $d=11-\frac{11}{2}=\frac{11}{2}$

Now, $x=a+(k-1)d\Rightarrow 550=\frac{11}{2}+(k-1)\frac{11}{2}\Rightarrow 550=k\frac{11}{2}\Rightarrow k=100$