The Step Counting Race

The story

Riya wanted to win a race by counting every single step upstairs, but the number of steps on each floor kept changing. Kabir challenged Riya to keep track all the way to the terrace, joking she would lose count by the third floor. Riya started counting each step, one by one, but Kabir joked she would never finish before dinner. As she counted, Riya noticed a pattern: the first floor had ten steps, the next had twelve, then fourteen. The difference was always two more steps per floor. She realised she could use a formula instead of counting every step. Was there a quicker way to find the total number of steps using this pattern?

The science

When numbers increase by a constant difference, they form an arithmetic progression. In this case, each floor has two more steps than the last. Instead of adding each number separately, you add the first and last terms, multiply by the number of terms, and divide by two. This gives the total quickly. The textbook term for this shortcut is arithmetic progression. This saves time and effort whenever you see a steady increase or decrease between numbers.

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