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  • Brainly User
2015-10-26T08:46:46+08:00

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Sum of series in Arithmetic Sequence:

S_{n} = \frac{n}{2} (a _{1} + a _{n})
Where:
S _{n} = is the sum of the series
n = term in a series ⇒ ?
a _{1} = is the first term, 2
a _{n} = 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 
    a _{n} = a _{1} + (n-1)(d)
    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:
     S _{n} =  \frac{14}{2} (2 + 28)&#10;
     S _{n}= 7 (30)
     S  _{n} = 210

The sum of the even numbers from 2 to 28 is 210.
     



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2015-11-01T23:58:21+08:00
2+4+6+8+10+12+14+16+18+20+22+24+26+28=30+30+30+30+30+30+30=210
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