A 14 foot ladder is leaning against a building. The ladder makes a 45 degree angle with the building. How for up the building does the ladder reach?

Step-by-step explanation:

Use trigonometry.

sin 45 degrees = x/14

plug in values and you get x =

, 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