How many 2-digit numbers are among the terms of the arithmetic sequence 2, 7, 12, 17, ... ?

20

Step-by-step explanation:

It seems like the rule of this sequence is to add 5 (since 2 + 5 = 7 and 7 + 5 = 12). We already are given that we have 2 2-digit numbers (12 and 17) so let's see if there are any more. The sequence continues to 22, 27, 32, 37, 42, 47, ..., 92, 97. We need to count how many numbers are in the list 2, 7 ... 92, 97. To do this, let's add 3 to every term in the list to get 5, 10, ... 95, 100. Since the list is now full of multiples of 5 we can divide the list by 5 to get 1, 2, ... 19, 20 which means that there are 20 2 - digit numbers.