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Sagot :
Sum of series in Arithmetic Sequence:
[tex]S_{n} = \frac{n}{2} (a _{1} + a _{n}) [/tex]
Where:
[tex]S _{n} [/tex] = is the sum of the series
n = term in a series ⇒ ?
[tex]a _{1} [/tex] = is the first term, 2
[tex]a _{n} [/tex] = is the last term, 28
Arithmetic series = {x/x is an even number<30}
Arithmetic sequence: {2, 4,...,28}
Even number, multiple of 2: the common difference (d) is 2
1) First, find the number of terms in the series
[tex]a _{n} = a _{1} + (n-1)(d)[/tex]
28 = 2 + (n-1)(2)
28 = 2 + 2n - 2
28 = 2n
28/2 = 2n/2
n = 14
The number of terms from 2 to 28 is 14.
2) Solve for the sum of the series:
[tex]S _{n} = \frac{14}{2} (2 + 28) [/tex]
[tex]S _{n}= 7 (30) [/tex]
[tex]S _{n} [/tex] = 210
The sum of the even numbers from 2 to 28 is 210.
[tex]S_{n} = \frac{n}{2} (a _{1} + a _{n}) [/tex]
Where:
[tex]S _{n} [/tex] = is the sum of the series
n = term in a series ⇒ ?
[tex]a _{1} [/tex] = is the first term, 2
[tex]a _{n} [/tex] = is the last term, 28
Arithmetic series = {x/x is an even number<30}
Arithmetic sequence: {2, 4,...,28}
Even number, multiple of 2: the common difference (d) is 2
1) First, find the number of terms in the series
[tex]a _{n} = a _{1} + (n-1)(d)[/tex]
28 = 2 + (n-1)(2)
28 = 2 + 2n - 2
28 = 2n
28/2 = 2n/2
n = 14
The number of terms from 2 to 28 is 14.
2) Solve for the sum of the series:
[tex]S _{n} = \frac{14}{2} (2 + 28) [/tex]
[tex]S _{n}= 7 (30) [/tex]
[tex]S _{n} [/tex] = 210
The sum of the even numbers from 2 to 28 is 210.
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