How many numbers are divisible by 9 in between 200 and 400?

There are 22 numbers divisible by 9 between 200 and 400.

Here's how to find that answer:

The reference tells us the numbers divisible by 9 between 200 and 400 begin with 207 and continue until 396: 207, 216, 225, .... 396. This sequence is an arithmetic progression where each term increases by 9.

To find the number of terms, we can use the formula for the nth term of an arithmetic sequence:

• a_n = a₁ + (n-1)d

Where:

• a_n is the last term (396)
• a₁ is the first term (207)
• n is the number of terms (what we want to find)
• d is the common difference (9)

Plugging in the values:

• 396 = 207 + (n - 1)9

Now, solve for 'n':

1. Subtract 207 from both sides:

   • 189 = (n - 1)9

2. Divide by 9:

   • 21 = n - 1

3. Add 1 to both sides:

   • n = 22

Therefore, there are 22 numbers divisible by 9 between 200 and 400.