S13 of -5+1+7...+67

Question

Find the indicated sum of each arithmetic series.

Answer 1

-5, 1, 7, 13, 19, 25, 31, 37, 43, 49, 55, 61, 67

S(n)=(n/2)(2a+[n-1]d) is the formula for the sum of an arithmetic sequence

S(13)=(13/2)(2*(-5)+[13-1]6)

S(13)=(13/2)(-10+72)

S(13)=(13/2)(62)

S(13)=13*31

S(13)=403

Answer 2

Erin,

 

It looks like this is a series that changes by 6

-5 + 1 + 7 + 13 + 19 + 25 + 31 + 37 + 43 + 49 + 55 + 61 + 67

 

For a total of 13 terms

 

We can write this using series notation as (admittedly this is the hardest step)

 

13

∑   6i-11

i-1

 

Recall

n
∑ i = (n)(n+1)/2
i-1

 

We can rewrite our series as

 

13
∑ 6i-11   = 

i-1

 

  13       13
6 ∑ i  -  ∑11  = 6(13)(14)/2 - 13(11) = 546 - 143 = 403 
  i-1     i=1