, , , ,

This is the formula to find the sum of the first terms of the sequence. To evaluate it, the values of the first and th terms must be found.

This is an arithmetic sequence since there is a common difference between each term. In this case, adding to the previous term in the sequence gives the next term. In other words, .

Arithmetic Sequence:

This is the formula of an arithmetic sequence.

Substitute in the values of and .

Apply the distributive property.

Combine and .

Combine and .

Move the negative in front of the fraction.

Combine the numerators over the common denominator.

Subtract from .

Divide by .

Add and .

Substitute in the value of to find the th term.

Replace the variables with the known values to find .

Combine the numerators over the common denominator.

Add and .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Combine and .

Multiply by .

Divide by .

Find the Sum of the Series 1/3 , 2/3 , 1 , 4/3 , 5/3