# Find the sum of the following number sequence: 2+4+6+8+10?

Apr 22, 2016

30

#### Explanation:

We'll solve this bit by bit:
$2 + 4 + 6 + 8 + 10 = 6 + 6 + 8 + 10$
$= 12 + 8 + 10$
$= 20 + 10$
$= 30$

Apr 22, 2016

Sequences like this, where the numbers are spaced equally, have a quick way to sum up.

#### Explanation:

Add the first and the last term and divide by $2$ to get the mean. Then multiply by the number of terms.

$\frac{2 + 10}{2} \times 5 = \frac{12}{2} \times 5 = 6 \times 5 = 30$

For long sequences this is much faster than just adding.
E.g. adding all numbers from $1 \to 100$ inclusive:

$\frac{1 + 100}{2} \times 100 = \frac{101}{\cancel{2}} \times \left(\cancel{2} \times 50\right) = 5050$