Question
Write the arithmetic series in summation notation.
7plus14plus21plus28
7plus14plus21plus28
Answers
Answered by
GPT-4o mini
The given arithmetic series is:
\[ 7 + 14 + 21 + 28 \]
To express this series in summation notation, we first identify the general term. The series can be observed as:
- The first term \( a = 7 \)
- The common difference \( d = 7 \) (since \( 14 - 7 = 7 \), \( 21 - 14 = 7 \), and so on)
The \( n \)-th term of an arithmetic series can be found using the formula:
\[
a_n = a + (n - 1)d
\]
For this series, it can be formulated as:
\[
a_n = 7 + (n - 1) \cdot 7 = 7n
\]
Now we need to determine the number of terms in the series. The series has four terms: \( 7, 14, 21, \) and \( 28 \) (which corresponds to \( n = 1, 2, 3, 4 \)).
Thus, the summation notation for the series can be written as:
\[
\sum_{n=1}^{4} 7n
\]
Therefore, the arithmetic series \( 7 + 14 + 21 + 28 \) in summation notation is:
\[
\sum_{n=1}^{4} 7n
\]
\[ 7 + 14 + 21 + 28 \]
To express this series in summation notation, we first identify the general term. The series can be observed as:
- The first term \( a = 7 \)
- The common difference \( d = 7 \) (since \( 14 - 7 = 7 \), \( 21 - 14 = 7 \), and so on)
The \( n \)-th term of an arithmetic series can be found using the formula:
\[
a_n = a + (n - 1)d
\]
For this series, it can be formulated as:
\[
a_n = 7 + (n - 1) \cdot 7 = 7n
\]
Now we need to determine the number of terms in the series. The series has four terms: \( 7, 14, 21, \) and \( 28 \) (which corresponds to \( n = 1, 2, 3, 4 \)).
Thus, the summation notation for the series can be written as:
\[
\sum_{n=1}^{4} 7n
\]
Therefore, the arithmetic series \( 7 + 14 + 21 + 28 \) in summation notation is:
\[
\sum_{n=1}^{4} 7n
\]