Sequences

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, ... -- What's the pattern of this sequence?

2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, ... -- What's the pattern of this sequence?

In a contest, such as "Are You Smarter than a Fifth-Grader?", you might be asked, "What's the next number in this sequence? 2, 3, 5". Can anyone figure out the answer?