Answer:
a) 3, 6, 9, 12, 15,...,
, b) 4, 7, 10, 13, 16,...,
, c) Both sequences are arithmetic.
Step-by-step explanation:
a) The sequence of natural numbers which are multiplied by 3 are represented by the function
,
. Let see the first five elements of the sequence: 3, 6, 9, 12, 15,...
b) The sequence of natural numbers which are multiplied by 3 and added to 1 is represented by the function
,
. Let see the first five elements of the sequence: 4, 7, 10, 13, 16,...
c) Both sequences since differences between consecutive elements is constant. Let prove this statement:
(i) 


(ii)

![\Delta f = [3\cdot (n+1)+1]-(3\cdot n+1)](https://tex.z-dn.net/?f=%5CDelta%20f%20%3D%20%5B3%5Ccdot%20%28n%2B1%29%2B1%5D-%283%5Ccdot%20n%2B1%29)

Both sequences are arithmetic.