Express the arithmetic sum using summation notation.

Question

Express the arithmetic sum using summation notation.
13 + 22 + 31 + + 184

k = 1

Answer 1

We need to find how many number we are adding.

a_n=a₁+(n-1)q

a_n=184, a₁=13.

The common difference q = 22 -13 = 9.

 

We replace these values in the equation (1) and find n.

184 = 13 +(n-1)9

184 - 13 = 9n - 9

171 = 9n-9

180 = 9n,

n = 20.

 

Here is the summation notation:

 

a_k=13+(k-1)9

Σ²⁰_k=1(a_k) =13 +22 + 31+ ... +184.

Answer 2

a1=13

a2=22

q=a2-a1=22-13=9 

 

Now

an=a1+(n-1)*q=184

 

Plug in q=9 and a1=13, and find n then for that n find Sn, Good luck, (if an problems let me know)