# How do you find the sum of the arithmetic sequence: 2,4,6,8,..., n = 20?

Mar 20, 2016

420

#### Explanation:

For the general Arithmetic sequence , with terms

a , a+d , a+2d , a+3d , .................... , a + (n-1)d

where a is the 1st term and d , the common difference

The sum to n terms =  n/2 [ 2a + (n-1)d) ]

here a = 2 , d = 4-2 = 6-4 = 2 and n = 20

sum of 1st 20 terms $= \frac{20}{2} \left[\left(2 \times 2\right) + \left(19 \times 2\right)\right] = 420$