the formula for an arithmetic sequence that is explicit is
where is the first term (so -1), and d is the common difference (-2). n is the number position in the sequence. As soon as we find the formula or model for this sequence we can find any number term we want. Filling in the formula:
and we'll clean that up just a bit:
(I just distributed through the parenthesis) and a bit more to
We first approach this problem by illustrating the situation. Refer to the diagram attached.
From the diagram, we can clearly see that we need to simply solve for the length marked x in order to find the distance between the foot of the ladder to the base of the wall.
Remember SOHCAHTOA. We can apply here the concept of cosine since we have the angle. Incorporationg x into the equation, we can simply make use of the relation cosine 72° = adjacent/hypotenuse.
ANSWER: The distance between the foot of the ladder and the base of the wall is 4.6 feet.