Answer:
S₆ = - 364
Step-by-step explanation:
the sum to n terms of a geometric series is
[tex]S_{n}[/tex] = [tex]\frac{a_{1}(r^{n}-1) }{r-1}[/tex]
where a₁ is the first term and r the common ratio
here a₁ = 2 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{-6}{2}[/tex] = - 3 , then
S₆ = [tex]\frac{2((-3)^{6}-1) }{-3-1}[/tex]
= [tex]\frac{2(729-1)}{-4}[/tex]
= [tex]\frac{2(728)}{-4}[/tex]
= [tex]\frac{1456}{-4}[/tex]
= - 364
