If the mean of the following data is 20, then the value of ‘a’ is

$\frac{{\displaystyle \sum f_i{x}_i}}{{\displaystyle \sum f_i}}=20$

$\frac{\left(2\times 15\right)+\left(3\times 17\right)+\left(4\times 19\right)+5a\times \left(20+a\right)+6\times 23}{2+3+4+5a+6}=20$

$\frac{30+51+76+100a+5a^2+138}{15+5a}=20$

$\frac{295+100a+5a^2}{5\left(a+3\right)}=20$

$\frac{5\left(59+20a+a^2\right)}{5\left(a+3\right)}=20$

$59+20a+a^2=20\left(a+3\right)$

$59+20a+a^2=20a+60$

$a^2=60-59$

$a^2=1$

$a=\sqrt{1}$

$a=1$