Algebra 2 Number Sequence?

Question

1) 7,9,15.33 
Find the next 5 terms in the sequence 

2) -2,3,27,69,129 
Find the next 2 terms in the sequence 

3) 1,7,21,46,85,141 
Find the next 3 terms in the sequence 

THANK YOU IN ADVANCE YOU GUYS

Answer 1

1).

Here is the answer for sequence 7, 9, 15, 33,.........

Rewrite the sequence as

To get the next five terms in the sequence, observe the above sequence

The sequence is .

2).

Here is the answer for sequence -2, 3, 27, 69, 129, .......

Rewrite the sequence as

To get the next two terms in the sequence, observe the above sequence

The sequence is .

3).

Here is the answer for sequence 1, 7, 21, 46, 85, 141, .......

Rewrite the sequence as 

1 - 7 = 6                     14 - 6 = 8                 11 - 8 = 3

21 - 7 = 14                 25 - 14 = 11                14 - 11 = 3      

46 - 21 = 25               39 - 25 = 14                17 - 14 = 3

85 - 46 = 39               56 - 39 = 17

141 - 85 = 56

To get the next three terms in the sequence, observe the above sequence

17 + 3 = 20 → 20 + 56 = 76 → 141 + 76 = 217

20 + 3 = 23 → 23 + 76 = 99 → 217 + 99 = 316

23 + 3 = 26 → 26 + 99 = 125 → 316 + 125 = 441.

The sequence is 1, 7, 21, 46, 85, 141, 217, 316, 441,...... .