How many 2-digit numbers are divisible by 4 in an arithmetic progression?

There are 22 two-digit numbers divisible by 4, forming an arithmetic progression.

Here's how we determine that:

• Identify the first 2-digit number divisible by 4: That's 12 (4 x 3).

• Identify the last 2-digit number divisible by 4: That's 96 (4 x 24).

• Recognize the arithmetic progression: The numbers divisible by 4 form an arithmetic progression with a common difference of 4: 12, 16, 20, ..., 96.

• Use the arithmetic progression formula: To find the number of terms (n) in an arithmetic progression, we can use the formula:

  Last term = First term + (n - 1) * Common difference

  96 = 12 + (n - 1) 4
  84 = (n - 1) 4
  21 = n - 1
  n = 22

Therefore, there are 22 two-digit numbers that are divisible by 4, which clearly follows an arithmetic progression since they are multiples of 4.