Geometric Sequences and Series

In a geometric sequence

each succesor term is the result of multiplying a fixed constant wit . Here is a concrete example, matched up with the natural numbers:

Here the starting point is 3 and the constant is 5. From these, called starting point and factor, respectively, every other term in the sequence is determined.

Develop the recursive function g-fives, which consumes a natural number and recursively determines the corresponding term in the above geometric sequence. Solution

Exercise 23.3.2

Develop the non-recursive function g-fives-closed. It consumes a natural number and determines the corresponding term in the above series. Solution

Exercise 23.3.3

Develop the function seq-g-fives, which consumes a natural number n and creates the sequence of the first n terms according to g-fives or g-fives-closed. Hint: Use build-list. Solution

Exercise 23.3.4

Develop geometric-series. The function consumes two numbers: start and s. Its result is a function that represents the geometric series whose starting point is start and whose factor is s. For example, (geometric-series 3 5) yields g-fives (or g-fives-closed). Solution

Exercise 23.3.5

Use series to determine the sum of the g-fives sequence for the bounds 3, 7, and 88. Use series to determine the sum of (geometric-series 1 .1) for the bounds 3, 7, 88. Can an infinite geometric series have a sum? Solution