Answer:
[tex]a_{7}[/tex] = - 160
Step-by-step explanation:
The n th term of a geometric sequence is calculated as
[tex]a_{n}[/tex] = a₁[tex](r)^{n-1}[/tex]
where a₁ is the first term and r the common ratio
Given
a₂ = - 5, then
a₁r = - 5, that is
2a₁ = - 5 ⇒ a₁ = - 2.5, thus
[tex]a_{7}[/tex] = - 2.5 × [tex](2)^{6}[/tex] = - 2.5 × 64 = - 160
