Question

Find $n$ if the given value of $x$ is the $n^{th}$ term of the AP: $5\frac{1}{2},11,16\frac{1}{2},22,...$ ; $x=550$.

• A. $100$
• B. $110$
• C. $200$
• D. $220$

Answer 1

Answer: (A)

$100$

Here, first term $a=5\frac{1}{2}=\frac{11}{2}$ and the common difference $d=11-\frac{11}{2}=\frac{11}{2}.$

Given, $a_n=x=550$
$\Rightarrow a+(n-1)d=550$

$\Rightarrow \frac{11}{2}+(n-1)\times \frac{11}{2}=550$

$\Rightarrow 1+(n-1)=550\times \frac{2}{11}$

$\Rightarrow n=100$