evaluate sigma from (n-1 to 14) 3n+2

The given series 3n + 2 represents an Arithmetic sequence. 

Consider the first few terms of the sequence.

For n = 1, the term is 5
For n = 2,  the term is 8
For n = 3, the term is 11

Notice that the difference between the terms is constant. Hence it is an arithmetic sequence. We are to find the sum of first 14 terms of the sequence.

The formula for the sum of AP is:

[tex]S_{n}= \frac{n}{2}(2a_{1}+(n-1)*d) [/tex]

n = number of terms = 14
a1 = first term = 5
d = common difference = 3

Using the values, we get:

[tex]S_{14}= \frac{14}{2}(2*5+(13)*3) \\ \\ S_{14}= 343[/tex]

So, the answer to this question is 343