The correct answers are:
(1) 6, 11, 16, 21, 26 (Option B)
(2)
;
(Option A)
(3)
(Option D)
Explanations:
(1) Given Sequence:

Now in order to find the first 5 terms, we need to put n=1,2,3,4,5 in the above sequence and solve.
For n=1: 
For n=2: 
For n=3: 
For n=4: 
For n=5: 
Hence, the first five terms are: 6, 11, 16, 21, 26 (Option B)
(2) Given Sequence:
8, 6, 4, 2, …
Now to find the recursive definition, we need to adopt trial-and-error approach.
As,
(meaning the first element of the sequence is 8), the second or nth value of the sequence can be found by using the following formula:
--- (1)
Where, n = the index of the number in a sequence
d = difference between two consecutive numbers = 8-6 = 2
Now,
The second number of the sequence has to be 6 by using (1). Put n = 2 and d = 2 in (1):


Since
, therefore,
(correct)
Hence the correct answer is
;
(Option A)
(3) Given Sequence:
−2, 1, 4, 7, …
To find the explicit definition, use the following formula:
--- (X)
Where,

Plug in the values in (X):
(X)=>
(Option D)