# How do you find the sum of the series 12i from i=0 to i=5?

Jan 21, 2017

You can add $12 \left(0\right) + 12 \left(1\right) + 12 \left(2\right) + 12 \left(3\right) + 12 \left(4\right) + 12 \left(5\right)$, or recognize a pattern and apply a formula.
What type of sequence is $0 , 12 , 24 , 36 , 48 , 60$?
Turns out that it is arithmetic, with a first term ${a}_{1}$ = 0, ${a}_{6} = 60$ and d = 12, with n = 6 terms.
${S}_{6} = \frac{6}{2} \left(0 + 60\right)$ = 3*60 = 180.