Lesson: Recursive Definitions of Terms

Here's my full solution: https://gre.myprepclub.com/forum/qotd-8-the-first-term-in-a-certain-sequ...

Cheers,
Brent

TWO OPTIONS:

OPTION 1: We'll use the fact that there are x - y + 1 integers from y to x inclusive.
Example: We want to determine how many multiples of 3 from 12 to 42 inclusive.
Notice that the multiples of 3 in question are: 12, 15, 18, . . . 39, 42.
We can rewrite these values as: 3(4), 3(5), 3(6), . . . , 3(13), 3(14)
So, the number of multiples is the number of integers from 4 to 14 inclusive, which is 14 - 4 + 1, which is 11.

OPTION 2: If M and N are multiples of k, then the number of multiples of k from M to N inclusive = [(M - N)/k] + 1
So, the multiples of 3 from 12 to 42 inclusive = [(42 - 12)/3] + 1
= [30/3] + 1
= 10 + 1
= 11