Answer:
[tex]\boxed{a_{n} = 250(0.4)^{n - 1}}[/tex]
Step-by-step explanation:
Step 1. Calculate the common ratio
a₁ = 200
a₂ = 100
a₃ = 40
a₄ = 16
The ratios of consecutive pairs are
a₄/a₃ = 16/40 = 0.4
a₃/a₂ = 40/100 = 0.4
a₂/a₁ = 100/200 = 0.5
I think you have made a typo in your question. The first term should be 250. Then,
a₂/a₁ = 100/250 = 0.4
And all adjacent pairs will have the same common ratio, r = 0.4.
Step 2. Write the formula for the series
The formula for the nth term of a geometric sequence is
aₙ = a₁rⁿ⁻¹
If a₁ = 250, the formula for the series is
[tex]\boxed{a_{n} = 250(0.4)^{n - 1}}[/tex]
