Write the sum using summation notation.
2 + 5 + 8 + 11 + ... + 29
Also, I know that it is going up by 3 units. But I am not sure how to get it into the form below:
example:
15
‡” k +3
k-1
you know the "formula" has to be 3n -1 to make it start at 2 when n=1
what must be n when 3n-1 = 29?
3n = 30
n = 10
so , (don't know how to make summation sign)
summation of 3n-1, n=1 at the bottom, 10 at the top of the sign.
Why did the number go to therapy?
Because it couldn't get into "sum" formation on its own!
But don't worry, I'll help you break it down. So the sum you have is:
2 + 5 + 8 + 11 + ... + 29
We notice that each term is increasing by 3 units, starting from 2.
To express this in summation notation, we can use the following form:
n
‡" (3k - 1)
k=1
So the sum, when written in summation notation, is:
n
‡" (3k - 1)
k=1
To write the sum using summation notation, we need to identify the pattern and the upper and lower limits. In this case, the pattern is that each term is 3 more than the previous term. The lower limit is the first term, which is 2, and the upper limit is the last term, which is 29.
The summation notation for this sum is:
∑(k=1 to 10) (3k - 1)
Let's break down the notation:
The Σ symbol represents the summation.
The variable k is the index or the iterator that represents the terms of the sum.
The number 1 below Σ represents the starting value of k.
The number 10 above Σ represents the ending value of k, which corresponds to the last term. Since the series goes up to 29, and each term is 3 more than the previous term, we can calculate the number of terms by subtracting the first term (2) from the last term (29) and then dividing by 3: (29 - 2) / 3 = 9. Therefore, the upper limit is 10 since we started counting k from 1.
The expression (3k - 1) represents the terms of the sum. k is the index or iterator, and (3k - 1) gives you each term in the series.
So, the summation notation for the given sum is:
∑(k=1 to 10) (3k - 1)
Note: The lower limit and upper limit can be adjusted accordingly depending on the starting and ending terms of the series.
To express the sum using summation notation, you can use the sigma symbol (∑) along with the appropriate expression inside it. In this case, the sum begins at 2, and each term is incremented by 3 until it reaches 29. Let's break down the components:
The index variable, often represented as "k", represents the position of each term in the sum. In this case, "k" will start from 1 and increase by 1 for each term.
The lower limit of the index, denoted as "k = ", will be 1 because the sum starts from the first term.
The upper limit of the index, denoted as "n", represents the position of the last term. In this case, it is the position of 29, which can be calculated as (29 - 2) / 3 + 1 = 10. So, "n = 10".
The expression to be summed is "k + 3". Since "k" represents the position and each term is incremented by 3, adding 3 to "k" will give us the corresponding value in the sequence.
Combining all the components, the summation notation for the given sequence can be expressed as:
∑ (k = 1 to 10) (k + 3)