Write 5+7+9+11+13+15+17 in sigma notation.
7
∑ (2i + 3)
i = 1
What is the common factor that we are adding each time?
so we're looking at something that looks like:
∑Number+2n
The "Number" will depend on where you want to start your summation. Usually, we begin from n = 0 or from n = 1. We'll need to make that choice now. Which would you like to do?
To write the expression 5+7+9+11+13+15+17 in sigma notation, we need to identify a pattern in the terms being added.
We can notice that each term is obtained by adding 2 to the previous term. Starting from the first term of 5, we add 2 to get the second term (7), then 2 more to get the third term (9), and so on.
Based on this pattern, we can write the sum of these terms in sigma notation as:
∑_(n=1)^(7) (2n + 3)
Here, the Greek letter sigma (∑) represents the sum, and n is the index of summation. The lower limit of the summation is 1 (the first term), and the upper limit is 7 (the seventh term).
Inside the summation, we have the term (2n + 3), where n takes on values from 1 to 7. This represents each term of the original expression, where 2n represents the increasing sequence (2, 4, 6, 8, 10, 12, 14), and adding 3 to each term gives us the desired sequence (5, 7, 9, 11, 13, 15, 17).
Therefore, the sum 5+7+9+11+13+15+17 can be represented as ∑_(n=1)^(7) (2n + 3) in sigma notation.