7, 9, 11, 13,15….

t50=t1+49d = 7+492=105

tn=t1+(n-1)d

Sn=

S50=

= 2800

Arithmetic Series

It’s  the sum of the terms in an arithmetic sequence with a definite number of terms.

for Example, the arithmetic sequence is : 1, 7, 13, 19, ….. 1 ,t1; 7, t2; 13, t3; 19, t4; etc, (ps: t=term)

then the Arithmetic Series will  be

S1= t1=1

S2=t1+t2=1+7=8

S3=t1+t2+t3=1+7+13=21

S4  1+7+13+19=40

you can do the simple math if there are just few number on the sequence, but if there are a lot, lie 30+ more term, there are two formula can be use, which can save a lot time and much easier.

Sn=n(t1+tn)/2,    or Sn=   (ps, the n is the number of the term, d is the difference between each term,)

1 . use the formula 1, the S6 for the up questions, we determine the t6 is =31， through d=6, then t6=t4+2d=19+2(6)= 31

the S6= 6(1+31)/2 = 96

use the 2nd formula , S6=6[2+6(5)]/2=98