Let the position count be #i#
Let any term be #a_i#
Let total count be #n#
So we have #a_1+a_2+a_3+...+a_n" "->" "4+8+12+...+312#
Notice that:
#8-4=4#
#12-8=4#
So really this is the sum of the 4 times table
#a_1=1xx4=4#
#a_2=2xx4=8#
#a_3=3xx4=13#
#a_n=nxx4=312 => n= 312/4 = 78#
#color(green)((1color(magenta)(xx4))+(2color(magenta)(xx4))+(3color(magenta)(xx4))+...+(78color(magenta)(xx4)))#
#color(magenta)(4)color(green)((1+2+3+..+78))#
'~~~~~~~~~~~~~~~~~~~
If you really wish to use mathematical notation
Given that the term #Sigma# means sum of and #Sigma_(i=1)^n a_i color(white)(.)# means sum of #a_1+a_2+...+a_n #
Then what we really have is #color(magenta)(4xx)color(green)(Sigma_(i=1)^78(i))#
The sum of #color(green)(1+2+3+...+78)" is count"xx"mean value"#
So we have
#color(green)(color(magenta)(4xx)Sigma_(i=1)^78(i))color(blue)(" "->" "color(magenta)(4)[78xx(1+78)/2] = color(magenta)(4xx)3081=12324)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(brown)("Demonstrating the principle")#
#Sigma_(i=1)^3(i) =1+2+3 =6" " ->" " 3xx(1+3)/2 =6#
#Sigma_(i=1)^4(i) = 1+2+3+4 = 10" "->" "4xx(1+4)/2 = 10#
#Sigma_(i=1)^5(i)=1+2+3+4+5=15" "->" "5xx(1+5)/2=15#
