provide a simple formula or rule that generates the terms of an integer sequence

Question

For the lists of integers, provide a simple formula or rule that generates the terms of an integer sequence that begins with the given list. Assuming that your formula or rule is correct, determine the next three terms of the sequence.

1. 3, 5, 8, 12, 17, 23, 30, 38, 47, . . .

Answer 1

....38, 46, 56, 67, 79, ....

a1=3

a2 =a1+2 = 3+2 = 5

a3 =a2+3 = 5+3 = 8

a4 = a3 +4 = 8+4 =12

a5 = a4 +5 = 12+5 = 17

a6 = a5+6 = 17+6 =23

a7 =a6 +7= 23+7 = 30

a8 =a7 +8 = 30+7 = 37

a9 = a8+9 = 37+9 = 46

a10 = a9 +10 = 46+10 = 56

a11 =a10+11 = 56 +11 = 67

an = a(n-1) + n

a11= 56+11 = 67