6. Find the sum of all even numbers from 10 to 31. Calculate in different ways.
6. Let's list all even numbers from 10 to 31:

$$
10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30
$$

a) Let's add the obtained numbers:

$$
10 + 12 + 14 + 16 + 18 + 20 + 22 + 24 + 26 + 28 + 30 = 220.
$$

b) We can notice that the sum of numbers equally distant from the ends is 40:

$$
10 + 30 = 12 + 28 = 14 + 26 = \ldots = 40
$$

There will be five such pairs, and the number 20 will remain. Let's calculate the sum:

$$
40 \times 5 + 20 = 220
$$

c) We can group the addends in such a way that their sum is a round number:

$$
\begin{gathered}
10 + 12 + 14 + 16 + 18 + 20 + 22 + 24 + 26 + 28 + 30 = \\
= 10 + (12 + 18) + (14 + 16) + 20 + (22 + 28) + (24 + 26) + 30 = \\
= 10 + 30 + 30 + 20 + 50 + 50 + 30 = 220
\end{gathered}
$$

Answer: The sum of all even numbers from 10 to 31 is 220.

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