In an arithmetic progression, the \(10^{th}\) term and \(16^{th}\) term are in the ratio \(5:7\). Calculate the ratio of the \(a_{6}\) term to the \(a_{22}\) term. Also compute the ratio of the sum of the first \(6\) terms to the sum of the first \(22\) terms.
 
t6:t22=i:i
 
S6:S22=i:i
 
(Note: Enter the ratios to its simplest form)