Answer:
<em>The common ratio of the geometric sequence is -4</em>
Step-by-step explanation:
<u>Geometric Sequence</u>
A geometric sequence is defined as a series of numbers that follow a fixed pattern: Each term equals the previous term times a fixed number called the common ratio. The recursive formula is:

Where r is the common ratio.
We are given three terms of a geometric sequence:
18,-72,288,...
To find the common ratio, just divide each term by the previous term:

Make sure it's a fixed number and test with the third term:

Since both numbers coincide, the common ratio of the geometric sequence is -4
The point is to find the growth rate. The compound formula is:
P=A(1+ growth rate)ⁿ, where A is the initial Value & P the new value after n years:
P₂₀₀₃ =P₂₀₀₂ (1+ growth rate)¹ (the period "n" from 2002 to 2003 being 1 year)
38400 = 32000(1+growth rate)¹
38400 / 32000 - 1= growth rate & growth rate = 1/5 = 0.2
You will balso find the same growth rate for:
P₂₀₀₄ = P₂₀₀₃(1+ growth rate)¹
P₂₀₀₅ = P₂₀₀₄((1+ growth rate)¹
between 2015 & 2002 THERE ARE 14 YEARS:
P₂₀₁₅ = P₂₀₀₂(1+0.2)¹⁴ & P₂₀₁₅ = 32000(1+02)¹⁴ = 410,854
Answer:
83.8 cm
Step-by-step explanation: