Question

at what position 2 comes in the arithmetic sequence 1/11,2/11,3/11 ?​

Answer 1

Given,

Arithmetic sequence $\[ = \frac{1}{{11}},\frac{2}{{11}},\frac{3}{{11}},\frac{4}{{11}}, - - - - \]$

Solution,

Consider the nth term of A.P. is 2.

$\[2 = \frac{1}{{11}} + (n - 1)\left( {\frac{2}{{11}} - \frac{1}{{11}}} \right)\]$

$\[ \Rightarrow 2 - \frac{1}{{11}} = (n - 1)\left( {\frac{1}{{11}}} \right)\]$

$\[\begin{array}{l} \Rightarrow \frac{{22 - 1}}{{11}} = (n - 1)\left( {\frac{1}{{11}}} \right)\\ \Rightarrow 21 = (n - 1)\\ \Rightarrow n = 1 + 21\\ \Rightarrow n = 22\end{array}\]$

Hence 2 will come at 22nd position of this Arithmetic sequence.