Astatement sn about the positive integers is given. write statements s1, s2, and s3, and show that each of these statements is true. show your work. sn:     12 + 42 + 72 + . . + (3n - 2)2 = n(6n^2-3n-1)/2

Explanation: 



To calculate for , note that the series is an arithmetic series because each term is equal to the preceding term plus a constant, which is 30 (called common difference). 

We let

 

Since  is an arithmetic series,  is an arithmetic sequence and so the formula for the nth term is given by



Where d = common difference = 30 

Now, since  is an arithmetic series, we can use the formula for the sum of the arithmetic series, which is given by