Notice that the common ratio between each term is -3.
So you have
[tex]S_7=2+(-6)+18+(-54)+\cdots[/tex]
[tex]S_7=2((-3)^0+(-3)^1+(-3)^2+(-3)^3+(-3)^4+(-3)^5+(-3)^6)[/tex]
[tex](-3)S_7=2((-3)^1+(-3)^2+(-3)^3+(-3)^4+(-3)^5+(-3)^6+(-3)^7)[/tex]
[tex]\implies(1-(-3))S_7=2((-3)^0-(-3)^7)[/tex]
[tex]\implies 4S_7=2(1-(-3)^7)[/tex]
[tex]\implies S_7=\dfrac{1-(-3)^7}2=1094[/tex]
