# How do you find the sum of the series 3i from i=1 to i=6?

Oct 23, 2016

The sum of the series is 63.

#### Explanation:

Use the summation property ${\sum}_{i}^{n} c {a}_{i} = c {\sum}_{i}^{n} {a}_{i}$, where c is a constant.

${\sum}_{1}^{6} 3 i = 3 \cdot {\sum}_{1}^{6} i$

Use the summation property ${\sum}_{x = 1}^{n} x = \frac{n \left(n + 1\right)}{2}$

$3 \cdot {\sum}_{1}^{6} i = 3 \cdot \frac{6 \left(6 + 1\right)}{2} = 63$

Alternatively, you could substitute i =1, i=2, i=3,...i=6 into 3i and then add.

$3 \left(1\right) + 3 \left(2\right) + 3 \left(3\right) + 3 \left(4\right) + 3 \left(5\right) + 3 \left(6\right) = 63$