Write the series using summation notation
5+11+17+23+29
The series can be written in summation notation as follows:
∑(n=1 to 5) (6n-1)
The series 5+11+17+23+29 can be written using summation notation as:
∑(i=1 to 5) (6i-1)
In this notation, the variable i represents the indices of the terms in the series. The upper limit of the summation is 5 since there are 5 terms in the series. The expression (6i-1) gives the value of each term in the series. By summing up all the terms from i=1 to i=5, you will obtain the original series.
To write the series using summation notation, we need to determine the pattern of the series and the number of terms.
In this case, we can observe that each term is obtained by adding 6 to the previous term. So, the common difference is 6.
The first term of the series is 5, and the number of terms in the series is 5.
Using this information, we can write the series using summation notation:
∑(n=1 to 5) (5 + (n-1)*6)
Let's break down the notation:
- The ∑ symbol represents the sum.
- 'n=1' indicates that the first term in the series is obtained when n = 1.
- '(n=1 to 5)' means that we sum up the terms starting from the first term (n=1) up to the fifth term (n=5).
- '(5 + (n-1) * 6)' represents the general term of the series, where n is the position of the term in the series.
Now, let's evaluate the summation notation:
∑(n=1 to 5) (5 + (n-1)*6) = (5 + (1-1)*6) + (5 + (2-1)*6) + (5 + (3-1)*6) + (5 + (4-1)*6) + (5 + (5-1)*6)
Simplifying this expression further, we get:
∑(n=1 to 5) (5 + (n-1)*6) = 5 + 5*6 + 5*2*6 + 5*3*6 + 5*4*6 + 5*5*6
Finally, calculating this expression gives us the sum of the series:
∑(n=1 to 5) (5 + (n-1)*6) = 5 + 30 + 60 + 90 + 120 + 150 = 455
Therefore, the series 5+11+17+23+29 can be written using summation notation as ∑(n=1 to 5) (5 + (n-1)*6), and its sum is 455.