Number patterns: find the rule

Find the missing term in the number pattern. Fifty-two thousand and three hundred. Fifty-one thousand and six hundred. Fifty thousand and nine hundred. Fifty thousand and two hundred. A missing term. Forty-eight thousand and eight hundred. Try it first. Pause if you like. The numbers are getting smaller. How much smaller is each term? Fifty-two thousand and three hundred minus fifty-one thousand and six hundred gives seven hundred. Check the next gap. Fifty-one thousand and six hundred minus fifty thousand and nine hundred is also seven hundred. Each term is seven hundred less than the previous. The missing term is fifty thousand and two hundred minus seven hundred, which is forty-nine thousand and five hundred. Notice the thousands. Subtracting seven hundred takes us below fifty thousand. Check: seven hundred less than forty-nine thousand and five hundred is forty-eight thousand and eight hundred. The rule tells us the size and the direction of each step.

Find the next term in the number pattern. Twenty thousand, eight hundred and fifteen. Twenty-one thousand, eight hundred and fifteen. Twenty-one thousand, seven hundred and fifteen. Twenty-two thousand, seven hundred and fifteen. Twenty-two thousand, six hundred and fifteen. Twenty-three thousand, six hundred and fifteen. Then a blank. Try it first. Pause if you like. This pattern rises, then falls. Do the gaps follow the same rule each time? The first gap is twenty-one thousand, eight hundred and fifteen minus twenty thousand, eight hundred and fifteen: one thousand. The second gap is twenty-one thousand, eight hundred and fifteen minus twenty-one thousand, seven hundred and fifteen: one hundred. The pattern is one thousand more, then one hundred less, repeated. One hundred less again. Then one thousand more again. The sixth term to the seventh term is one hundred less. The seventh term is twenty-three thousand, six hundred and fifteen minus one hundred: twenty-three thousand, five hundred and fifteen. Find the gaps and follow their direction. When two steps take turns, the pair is the rule.