Question 1139868
 the sum of all even numbers from {{{4}}} to {{{100}}} inclusive, excluding those which are multiples of {{{3}}}.


We have to find the number of terms that are divisible by {{{2}}} but not by {{{6 }}}( as the question asks for the even numbers only which are not divisible by {{{3}}})

For {{{2}}},

{{{4}}},{{{6}}},{{{8}}},.........,{{{100}}}

using AP formula, we can say {{{100 = 4 + (n-1) *2}}}

{{{100-4=(n-1) *2}}}

{{{96/2=n-1}}}

{{{48+1=n}}}

 {{{n=49 }}}

For {{{6}}},

{{{6}}},{{{12}}},{{{18}}},......{{{96}}}

using AP formula, we can say {{{96 =6+ (n-1) *6}}}

{{{96-6=(n-1)*6}}}

{{{90/6=n-1}}}

{{{15+1=n}}}

{{{n=16}}} 


{{{49-16=33 }}} is the number of terms that are divisible by {{{2}}} but not by {{{6}}}

here are they: all divisible by {{{2}}},  highlighted divisible by {{{6}}}

{{{4}}}, {{{highlight(6)}}}, {{{8}}}, {{{10}}}, {{{highlight(12)}}}, {{{14}}}, {{{16}}},{{{highlight( 18)}}}, {{{20}}}, {{{22}}}, {{{highlight(24)}}}, {{{26}}}, {{{28}}}, {{{highlight(30)}}}, {{{32}}}, {{{34}}}, {{{highlight(36)}}}, {{{38}}}, {{{40}}}, {{{highlight(42)}}}, {{{44}}}, {{{46}}}, {{{highlight(48)}}},{{{ 50}}}, {{{52}}}, {{{highlight(54)}}}, {{{56}}}, {{{58}}},{{{highlight( 60)}}}, {{{62}}},{{{ 64}}},{{{highlight( 66)}}},{{{ 68}}}, {{{70}}},{{{highlight( 72)}}}, {{{74}}}, {{{76}}}, {{{highlight(78)}}}, {{{80}}},{{{ 82}}}, {{{highlight(84)}}},{{{ 86}}}, {{{88}}}, {{{highlight(90)}}},{{{ 92}}},{{{ 94}}}, {{{highlight(96)}}},{{{98}}},{{{100}}}


now add all {{{33 }}} numbers that are not highlighted

{{{4+ 8+10+14+16+ 20+ 22+ 26+28+32+34+ 38+40+ 44+46+ 50+52+56+58+ 62+64+68+70+74+76+80+82+86+88+92+94+98+100=1732}}}