Calculate s75 for the arithmetic sequence defined by

The value of is -675 and this can be determined by using the formula of the sum of n terms in the arithmetic sequence and the given data.

Given :

  --- (1)

The following steps can be used in order to determine the value of :

Step 1 - Substitute the value of (n = 1) in the expression (1).

Step 2 - Substitute the value of (n = 75) in the expression (1).

Step 3 - Now, the formula of sum in an arithmetic sequence is given below:

where n is the total number of terms, is the first term, and is the last term.

Step 4 - Substitute the values of the known terms in the above expression.

Step 5 - Simply the above expression.

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The formula of a sum of an arithmetic sequence:

We have n = 75 and .

Calculate the first and seventy-fifth term:

Substitute: