The arithmetic series is 34 + 30 + 26 +  .... + 2.

The nth term of an arithmetic sequence is .

Where is first term of the sequence and d is common difference.

Here .

Common difference ,

So .

The nth term of an arithmetic sequence is .

               (Substitute )

Distribute terms using distributive property: .

                         (Product of two same signs is positive)

                           (Add: 34 + 4 = 38)

Apply subtraction property of equality: a = b then .

           (Subtract 38 from each side)

                     (Apply additive inverse property: )

                           (Apply additive identity property: )

                              (Subtract: )

Apply division property of equality: a = b then .

                         (Divide each side by negative 4)

                                 (Cancel common terms)

n = 9                                          (Divide: )

The sum of an arithmetic series .

Where is the first term and is the nth term.

                       (Substitute )

                            (Add: 34 + 2 = 36)

                               (Multiply: )

                                  (Divide: )

The sum of the arithmetic series is 162.