Arithmetic Sequences

Gauss’s trick

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Arithmetic sequence: $a_n = a + (n-1)d$.
• Sum = number of terms × average of the first and last terms. In particular, $1 + \cdots + n = \frac{n(n+1)}{2}$.
• The sum of the first $n$ odd numbers is $n^2$.

Steps

1. The schoolboy’s sum
2. Picture the trick
3. Arithmetic sequences
4. The 50th term
5. Every fourth number
6. Odd numbers