Number sequences

In your book, Maths Mela (Chapter 1), there are rows of numbers that follow a pattern, and we have to fill in the next ones. To continue a pattern, first find the STEP: how much the numbers change from one to the next.

Take 456, 567, 678. From 456 to 567 is 111 more, and from 567 to 678 is 111 more again. So the step is 'up by 111', and the next numbers are 678 + 111 = 789 and 789 + 111 = 900.

Sometimes a number in the middle is missing: 1,050, __, 3,150, 4,200. The last two numbers show the step: 4,200 − 3,150 = 1,050. So the missing number is 1,050 + 1,050 = 2,100. Check: 2,100 + 1,050 = 3,150. It fits.

A pattern can also go DOWN. In 73,005, 72,004, the ten thousands stay 7, the thousands go from 3 to 2 and the ones go from 5 to 4. So each step is 1,000 less and 1 less: down by 1,001. The next numbers are 71,003 and 70,002.

Always check the step between more than one pair of numbers. In 5,501, 6,401, 7,301 the step is not 1,000 but 900: 5,501 + 900 = 6,401, and 6,401 + 900 = 7,301.