If ${\displaystyle \sum _{j=1}^{21}{a}_j}=693$  where $a_1,a_2,a_3\mathrm{........}{a}_{21}$ are in A.P. then $\sum _{i=0}^{10}{a}_{2i+1}=\_\_\_\_\_$ 

${\displaystyle \sum _{j=1}^{21}{a}_j}=693$

$a_1+a_2+a_3+\mathrm{......}+a_{11}+\mathrm{.......}+a_2{}_1=693$

$10\left(a_1+a_{21}\right)+a_{11}=693$

$\left(\because A.M=\frac{693}{21}=33\right)$

$10\left(a_1+a_{21}\right)+33=693$

$a_1+a_{21}=66$

${\displaystyle \sum _{i=0}^{10}{a}_{2i+1}}=a_1+a_3+a_5+\mathrm{......}+a_{21}$

$=5\times \left(a_1+a_{21}\right)+a_{11}$

$=5\times 66+33=363$