Jason observed a large art sculpture in a local park and wanted to know its height, but the sculpture was much taller than he could measure. Jason measured the length of the shadow of the sculpture's highest point to be 15 feet long. If the top of a slide in the same park, measured at the same time of day, has a height of 75 inches and a shadow length of 45 inches, how tall is the art sculpture at its highest point?

A. 30 feet
B. 20 feet
C. 25 feet
D. 45 feet

, 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