Answer:
S₇ = 127
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 = 1 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{2}{1}[/tex] = 2 , then
S₇ = [tex]\frac{1(2^7-1)}{2-1}[/tex] = [tex]\frac{2^7-1}{1}[/tex] = [tex]2^{7}[/tex] - 1 = 128 - 1 = 127
