Write 10+6+2+(-2)+(-6)+(-10)+(-14) in sigma notation.
Sigma n=0 to 6 of (10-4n)
wait how can I write that in a paper?
geez - look at some examples
6
∑ 10-4n
n=0
To write the given expression in sigma notation, we need to identify the pattern and define the limits of the series.
The pattern in the terms is that the coefficients are decreasing by 4 each time, starting from 10. The series can be written as:
Σ(10 + (-4n)), where n starts from 0 and goes to 6.
Let's break it down step by step:
1. The first term is 10 when n = 0, so it becomes 10 + (-4 * 0) = 10 + 0 = 10.
2. The second term is 6 when n = 1, so it becomes 10 + (-4 * 1) = 10 + (-4) = 6.
3. The third term is 2 when n = 2, so it becomes 10 + (-4 * 2) = 10 + (-8) = 2.
4. The fourth term is -2 when n = 3, so it becomes 10 + (-4 * 3) = 10 + (-12) = -2.
5. The fifth term is -6 when n = 4, so it becomes 10 + (-4 * 4) = 10 + (-16) = -6.
6. The sixth term is -10 when n = 5, so it becomes 10 + (-4 * 5) = 10 + (-20) = -10.
7. The seventh term is -14 when n = 6, so it becomes 10 + (-4 * 6) = 10 + (-24) = -14.
Therefore, the expression 10+6+2+(-2)+(-6)+(-10)+(-14) can be written in Sigma notation as Σ(10 + (-4n)), where n = 0 to 6.