If `a_(1),a_(2),a_(3),"........"` is an arithmetic progression with common difference 1 and `a_(1)+a_(2)+a_(3)+"..."+a_(98)=137`, then find the value of `a_(2)+a_(4)+a_(6)+"..."+a_(98)`.

Explanation

`a_(1)+a_(2)+"....."+a_(98)=137`
`(98)/(2)(a_(1)+a_(98))=137`
`a_(1)+a_(2)+97=(137)/(49),2a_(1)+97=(137)/(49)`
`2a_(1)=(137)/(49)-97,a_(1)=(1)/(2)(137-4753)/(49)`
`a_(1)=-(4616)/(2xx49),a_(1)=(2308)/(49)" " "........(i)"`
`a_(2)+a_(4)+"......+"a_(98)=(a_(1)+1)+(a_(1)+3)+"........"+(a_(1)+97)" "[:.d=1]`
`49a_(1)+(1+3+"......."+97)`
`=-49xx(2308)/(49)+(49)/(2)(1+97)`
`=-2308+49^(2)`
`=-2308+2401=93`.