1 Determine the sum of the series:
.

To determine the sum of each of the series, let’s analyze both sequentially.

1.1 The series is an arithmetic series where the first term and the common difference . The last term is . To find the number of terms , we can use the nth-term formula of an arithmetic sequence:

Setting :

Solving gives:

Now, using the sum formula for an arithmetic series:

Substituting the values:

1.3 The series is another arithmetic series where the first term and the common difference . To find the number of terms , we use the last term:
Setting :

Solving gives:

Now, using the sum formula:

Substituting the values:

So, the sums of the series are:
1.1. -4650
1.3. 1090