Question

Write the sum using summation notation, assuming the suggested pattern continues.

Answer 1

Thank you for posting your question here. Below is the sum of the pattern above using the summation notation. 

4 + 5 + 14 + 23 +...+1 31 = ∑n=015(−4)+n⋅9

Summation Notation. Often mathematical formula require the addition of many variables Summation or sigma notation is a convenient and simple form of shorthand used to give a concise expression for a sum of the values of a variable.

Answer 2

Answer:

$\sum_{n=0]^{15}(-4+9n)$.

Step-by-step explanation:

First, we need to find the pattern. From -4 to 5 there are 9 units, also from 5 to 14 and from 14 to 23. Then, the pattern is add 9 units to the previous term.

That is, the sum is of the form -4 + 9n.

Now, we need to find how many terms there are in the sum to find the upper limit of n.

131 = -4 + 9n

131 +4 = 9n

135 = 9n

n = 135/9 = 15.

Then, the sum goes from n= 0 to n = 15. Finally, the notation will be

$\sum_{n=0}^{15}(-4+9n)$.