Kabuuan o sum ng mga even number na hindi lalampas ng 30

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.
     



2+4+6+8+10+12+14+16+18+20+22+24+26+28=30+30+30+30+30+30+30=210