A map provided by an engineering firm has a scale of 1 inch to 2000 feet. If the distance from the starting point for a pipeline to the ending point is 13 1/2 inches how long is the pipe line?

27,000 feet

Step-by-step explanation:

Let be the actual length of the pipeline, in feet.

Set up the following proportion:

Cross-multiplying yields

step-by-step explanation:

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for