Chapter 8.4A, Problem 10A

For each of the following sequences(either arithmetic or geometric), (i) find a possible function $f\left(n\right)$ whose domain is the set of natural number and whose outputs are the terms of the sequence, (ii) find the sum of the first $20$ terms of each sequence.

a. $3,8,13,18,23\dots$

b. $3,9,27,81,243\dots$

c. $3,3,3,3\dots$

d. $3,3^{\frac{4}{3}},3^{\frac{5}{3}},3^2$