How I do patterns?

Question

Here are 10 different patterns or sequence of letters and numerals. Some of them are not a sequence using standard operations of addition or multiplication. Consider each of them carefully and look for other reasons that the pattern was established.



To Do:

1) find the next three elements in the sequence

2) give a very brief explanation (or process) for determining what comes next. In other words, explain the pattern.



1. 1, 10, 100, 1000,







2. 0, 10, 21, 33, 46, 60,







3. 1, 4, 9, 16, 25,







4. 1, 1, 2, 3, 5, 8, 13,







5. 1, 3, 6, 10, 15, 21,







6. 1, 3, 7, 15, 31, 63,







7. 18, 46, 94, 63, 52, 61,







8. O, T, T, F, F, S, S,







9. A, 2, B, 0, C, 2, D, 0, E, 3, F, 3, G,







10. A, B, D, G, K,

Answer 1

1] increase the exponent of 10 by 1 for the next value
2] increase the value by adding sequential whole numbers starting with 10 i.e. the numbers to add are 10, 11, 12, 13, etc
3] increase the value by adding sequential prime numbers starting with 3 i.e. 3,5,7,9,11, 13, etc
4] add the increase numbers to generate next increase number i.e. 0,1,1,2,3,5,8 etc so 0+1=1, then 1+1=2, then 1+2=3, etc
5] increase the values with sequential numbers starting with 2 i.e. 2,3,4,5,etc
6] double the increase number and use the result as next increase number i.e. increase by 2, 4, 8, 16, 32 etc
7] no idea
8] no idea
9] no idea for numbers, but letters just keep going along in alphabet
10] remove 0 letters, then 1 letter, then 2 letters, then 3, etc

Answer 2

3,1,4,9,16,25