Do you have to plug in numbers to make a sequence that is greater than 2?? Solve!

2 or greater

a.  The formula  is   a_n =    a_n-1 - 3....so   a₂ = a_2-1 - 3  =  a₁ - 3

Notice GM  that we are just subtacting 3 from the previous term to get the next....and the first term is 7...so

7, 4, 1 , -2

This is arithmetic

b.  The formula  is  b_n = 2b_n-1  - 1   .....so    b₂ = 2b_(2-1) - 1  =  2b₁ - 1

We are taking  twice the previous term and subtracting 1 to get the next term and the first term is  2

So we have

2, 3, 5, 9

This is neither

c. The formula is  c_n  = 10c_n-1   ...  so.....c₂  = 10 c_{(2 - 1)}  = 10c₁

So....we are just taking 10 times the previous term to h=get the next 

So      3, 30, 300, 3000

geometric

d.   A little tricky.....

We have

 d_n  = n * d_n-1   .....  first term is  1

Second term...n = 2      

d₂ = 2 * d_n-1   =    2 * d_{(2 - 1)}  =  2 * d₁  = 2 * 1  =  2

d₃  =   3* d₂  =  3 * 2  = 6

d₄  = 4 * d₃  = 4 * 6 = 24

So we have

1, 2, 6 , 24

neither......no common difference or common ratio