Question

Can someone please help me find the geometric sequence of

Answer 1

Answer:

$\boxed{a_{n} = 250(0.4)^{n - 1}}$

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

$\boxed{a_{n} = 250(0.4)^{n - 1}}$