Answer:
see explanation
Explanation:
The n th term of a geometric sequence is
= a
where a is the first term and r the common ratio
Both a and r have to be found
Given a₃ = - 2, then
ar² = - 2 → (1)
Given a₇ = - 32, then
a = - 32 → (2)
Divide (2) by (1)
= , that is
= 16 ( take the fourth root of both sides )
r = 2 ← common ratio
Substitute r = 2 into (1)
a × 2² = - 2, that is
4a = - 2 ( divide both sides by 4 )
a = - ← first term
Hence
= - ← explicit formula
and
= - × = - 0.5 × 512 = - 256
Explanation: