Answer:
a₁ = 8 and r = 16
Step-by-step explanation:
the sequence has a common ratio r between consecutive terms and is therefore geometric , that is
r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{2^{7} }{2^3}[/tex] = [tex]2^{(7-3)}[/tex] = [tex]2^{4}[/tex] = 16
r = [tex]\frac{a_{3} }{a_{2} }[/tex] = [tex]\frac{2^{11} }{2^7}[/tex] = [tex]2^{(11-7)}[/tex] = [tex]2^{4}[/tex] = 16
r = [tex]\frac{a_{4} }{a_{3} }[/tex] = [tex]\frac{2^{15} }{2^{11} }[/tex] = [tex]2^{(15-11)}[/tex] = [tex]2^{4}[/tex] = 16
the first term a₁ = 2³ = 8