1. 5. Each number represents a letter of the alphabet, so the series says WELCOME.
2. 7. The numbers in the series will be displayed if you divide 6 by 17.
3. 60. 100 years in a century, 365 days in a year, 24 hours in a day, 60 minutes in an hour, & 60 seconds in a minute.
4. 133. A very tough one! The numbers represent the odd prime numbers, multiplied by the number for their place in the series of odd prime numbers. 3 is the first odd prime number, & because it is first, it is multiplied by 1; 5 is the second odd prime number, & is thus multiplied by 2, which yields 10, & so on.
5. 8. Beginning with Sunday, each number represents the number of letters in each day of the week.
6. 3. Each number is the number of letters in the word for each number from ONE to TEN.
7. 8. Each number is the number of letters in each month of the year, beginning with January.
8. 1. Skipping the number 3, the series is pi reversed.
9. 9. Each number represents the first number found after the decimal point when one number is divided by another. The first number, 5 is for 1/2; 6 is for 2/3, 7 is for 3/4, 8 is for 4/5, & so on.
10. 11. This puzzle is similar to the last one. The numbers represent the numbers immediately before and after the decimal point, but 0's are not shown. The first number, 2, is for 2/1; 15 is for 3/2, 13 is for 4/3, & so on.
11. 654431. Each number is shown in reverse. After 8, each number represents the product after 8 is consecutively multiplied by 7.
12. 803. The first number is 22, but you subtract 1 from the last number, & add it to the first number. Double 22, & then perform the same procedure, & you have 53, & so on.
13. 3. After adding 1 to 2, the first number, an additional number is added to each resulting number, yielding 3, 5, 8, 12, etc. The first number is written on the far left, the second number is on the far right, the third number is second from the left, the fourth number is second from the right, & so on.
14. .00513216. Multiply the first number, 6, by 66, which yields 396; multiply 396 by 6, & then multiply the product of this by .06, & the product of that by .006.