List the first 10 terms of each of these sequences.
a. the sequence obtained by starting with 10 and obtaining each term by subtracting 3 from the previous term
b. the sequence whose nth term is the sum of the first n positive integers
c. the sequence whose nth term is 3n − 2n
d. the sequence whose nth term is √ n
e. the sequence whose first two terms are 1 and 5 and each succeeding term is the sum of the two previous terms

A. We start by writting down the general formula:
a(1) = 10
a(2) = a(1) - 3  
a(3) = a(2) - 3
a(n) = a(n-1) -3

Now we find first ten terms:
10, 7, 4 ,1, -2, -5, -8, -11, -14, -17

b. We start by writting down the general formula:
a(1) = 1
a(2) = 1 + 2
a(3) = 1 + 2 + 3
a(n) = 1 + 2 + ... + n

Now we find first ten terms:
1, 3, 6, 10, 15, 21, 28, 36, 45, 55

c. We start by writting down the general formula:
a(n) = 3n -2n = n

Now we find first ten terms:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10

d. We start by writting down the general formula:


Now we find first ten terms:


e. We start by writting down the general formula:
a(1) = 1
a(2) = 5
a(3) = a(1) + a(2)
a(4) = a(2) + a(3)
a(n) = a(n-2) + a(n-1)

Now we find first ten terms:
1, 5, 6, 11, 17, 28, 45, 73, 118, 191

How many groups are there?