Question 866321
the number is of the form {{{4x+1}}} by definition where {{{x}}} is a natural number 

 first such 2 digit number is {{{4*3+1=13 }}}
 last such 2 digit number is {{{4*24+1=97 }}}


this is an arithmetic progression with common difference {{{4}}} 

so, we have {{{13}}},{{{17}}},{{{21}}},{{{25}}},{{{29}}},{{{33}}},{{{37}}],{{{41}}},{{{45}}},{{{49}}},{{{53}}},{{{57}}},{{{61}}},{{{65}}},{{{69}}},{{{73}}},{{{77}}},{{{81}}},{{{85}}},{{{89}}},{{{93}}},{{{97}}}

the sum is given by {{{sum=(n/2)(2a+(n-1)*d) }}}

{{{n}}} is the number of terms, {{{a}}} is the first number, {{{d}}} is the common difference 

{{{n=(97-13)/4+1=22 }}}  
{{{a=13}}} 
{{{d=4}}} 
{{{sum=(22/2)*(2*13+21*4)= 11(110)=1210 }}}