Answer:
a₄ = [tex]\frac{8}{125}[/tex]
Step-by-step explanation:
the nth term of a geometric sequence is
[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]
a₁ is the first term, r the common ratio, n the term position
here a₁ = 1 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{\frac{2}{5} }{1}[/tex] = [tex]\frac{2}{5}[/tex] , then
[tex]a_{n}[/tex] = 1 [tex](\frac{2}{5}) ^{n-1}[/tex]
using the nth term formula to find a₄
a₄ = 1 × ( [tex]\frac{2}{5}[/tex] )³ = [tex]\frac{2^{3} }{5^{3} }[/tex] = [tex]\frac{8}{125}[/tex]
